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  • 1
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 13-23 
    ISSN: 0271-2091
    Keywords: Adaptive Finite Element Method ; Combustion ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An adaptive finite element method is developed and applied to study the ozone decomposition laminar flame. The method uses a semidiscrete, linear Galerkin approximation in which the size of the elements is controlled by an integral which minimizes the changes in mesh spacing. The sizes and locations of the elements are controlled by the location and magnitude of the largest temperature gradient. The numerical results obtained with this adaptive finite element method are compared with those obtained using fixed-node finite-difference schemes and an adaptive finite-difference method. It is shown that the adaptive finite element method developed here using 36 elements can yield as accurate flame speeds as fourth-order accurate, fixed-node, finite-difference methods when 272 collocation points are employed in the calculations.
    Additional Material: 10 Ill.
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 71-80 
    ISSN: 0271-2091
    Keywords: Finite Difference ; Residual Method ; Elliptic Equation ; Cavity Flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A residual method of finite differencing the governing differential equation for the elliptic transport problem is presented. The new finite differencing technique is applied to (1) the one-dimensional transport problem and (2) the cavity flow problem for numerical illustrations. The results indicate the validity of the residual method of finite differencing. The usual method of term-by-term finite differencing, and considerations such as central differencing, hybrid differencing and upwind differencing are not needed in the present residual method.
    Additional Material: 7 Ill.
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 99-99 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 81-97 
    ISSN: 0271-2091
    Keywords: Compressible Flow ; Turbulent Flow ; Boundary Layers ; Galerkin Method ; Spline Functions ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The applicability of a finite element-differential method to the computation of steady two-dimensional low-speed, transonic and supersonic turbulent boundary-layer flows is investigated. The turbulence model chosen for the Reynolds shear stress and turbulent heat flux is the K-∊ two-equation model. Calculations are extended up to the wall and the exact values of the dependent variables at the wall are used as boundary conditions. A number of transformations are carried out and the assumed solutions at a longitudinal station are represented by complete cubic spline functions. In essence, the method converts the governing partial differential equations into a system of ordinary differential equations by a weighted residuals method and invokes an ordinary differential equation solver for the numerical integration of the reduced initial-value problem. The results of the computations reveal that the method is highly accurate and efficient. Furthermore, the accuracy and applicability of the k-∊ turbulence model are examined by comparing results of the computations with experimental data. The agreement is very good.
    Additional Material: 8 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 100-100 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 101-114 
    ISSN: 0271-2091
    Keywords: Turbomachines ; Finite Elements ; Transonic Flows ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper describes the extension of a purely two-dimensional finite element method for the calculation of transonic turbomachinery blade-to-blade flows to include the quasi-three-dimensional terms. These terms account for the effect of variations in streamline radius, stream-tube height and blade rotation.By approximating the stream surface as a piecewise linear function, then using a local developed cone transformation on an element basis, the finite element equations are shown to remain of the same form as the two-dimensional equations.The numerical results presented demonstrate that the stream-tube height, streamline radius and blade rotation terms must be included if the prediction of the Mach number distribution around a gas turbine blade is to be calculated correctly.
    Additional Material: 9 Ill.
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 115-132 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Steady two-dimensional transonic flow is calculated in cascades of compressor and turbine blades using a mesh of triangular finite elements. A velocity potential is used, the equations being solved by the Newton-Raphson technique. The resulting computer program is fast, and is shown to give good accuracy. Shock waves are well represented, provided they are not too strong.
    Additional Material: 16 Ill.
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  • 8
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 133-154 
    ISSN: 0271-2091
    Keywords: Thermal Convection ; Rotating Channel Flow ; Finite Difference Method ; Secondary Flows ; Rotational Instabilities ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical study is conducted on the effect of sidewall heating in the pressure-driven laminar flow of an incompressible viscous fluid through a rectangular channel that is subjected to a spanwise rotation. The time-dependent Navier-Stokes equations are solved along with the conservation equations for energy and mass by a finite-difference technique. The effect of weak to moderate sidewall heating on the overall flow structure at different rotation rates is studied. It is observed that for weak sidewall heating, the secondary flow structure is quite similar to the corresponding isothermal case. However, when the sidewall heating is moderate, various types of secondary flow fields are found to occur depending on the magnitude of the rotation. The influence of rotational speed on the net heat transport for different levels of sidewall heating is also studied. It is found that when the sidewall heating is weak, the basic secondary flow structure for the non-rotating case is of a unicellular form and an increase in the rotation speed leads to an increase in the net heat transfer due mainly to the rotationally driven transport of fluid from the high temperature to the low temperature region. On the other hand, when the sidewall heating is moderate so that the basic secondary flow structure for the non-rotating case has a multicellular configuration, an increase in the rotation speed leads to a decrease in the heat transport due to the weakening of the shear layer near the hot wall.
    Additional Material: 25 Ill.
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  • 9
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 169-189 
    ISSN: 0271-2091
    Keywords: Jeffery-Hamel ; Orr-Sommerfeld ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An asymptotic scheme is presented for the solution of the steady state and time dependent stream functions for flows in symmetric curved walled channels. In this scheme a class of non-linear Jeffery-Hamel solutions appear at O(1), and thus provide the first approximation to the steady state stream function. This class of Jeffery-Hamel solutions are evaluated by using a simple perturbation about Poiseuille flow.The classic Orr-Sommerfeld eigenproblem appears at O(1) in the asymptotic development of the time dependent stream function, but here there is a slow streamwise dependence. This eigenvalue problem, for a complex wave number, is solved using an algorithm which automatically provides an initial guess which is then used to iterate to the correct eigenvalue.Higher order terms in the asymptotic development, for both the steady state and time dependent stream functions, are evaluated to provide a solution for the total stream function.
    Additional Material: 8 Ill.
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  • 10
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 155-167 
    ISSN: 0271-2091
    Keywords: Turbulent Flow ; Tri-cusped Duct ; Finite Volume ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An orthogonal-cuvilinear-mesh-based finite volume calculation method has been applied to the problem of fully developed turbulent flow in the tri-cusped cornered duct formed when parallel circular rods touch in triangular array. Algebraic stress relations combined with the k-∊ turbulence model are used for calculation of the required stresses. A single circulation of turbulence-driven cross-plane secondary flow from the core into the duct corner has been predicted in a one-sixth symmetry region of the duct and the convective transport effects of this flow are seen to have much influence on local mean flow distributions. The turbulence field predicted by the k-∊ model showed significant damping in the cusped corner region where turbulent viscosities approached the laminar value. Satisfactory agreement was obtained with the limited local and overall mean flow measurements available.
    Additional Material: 12 Ill.
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  • 11
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 331-345 
    ISSN: 0271-2091
    Keywords: Turbomachines ; Design ; Finite Element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper the development of a compatible mixed design and analysis method is presented for the quasi-three-dimensional finite element blade-to-blade program FINSUP. The method consists of two parts. The first is concerned with a method of modelling changes to a blade shape using a surface transpiration model. The second is concerned with determining the relationship between the displaced blade surface and the surface velocity distribution. It is shown that with the Newton-Raphson procedure adopted in the method a very efficient manner of introducing the design option is possible. As a consequence the resulting program is fast and completely interactive. A number of examples are given to illustrate how the mixed design and analysis mode can be used in practical blade design.
    Additional Material: 16 Ill.
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  • 12
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 311-329 
    ISSN: 0271-2091
    Keywords: Cavity Flows ; Finite-differences ; Numerical Accuracy ; Velocity Measurements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical and an experimental study of the flow of an incompressible fluid in a polar cavity is presented. The experiments included flow visualization, in two perpendicular planes, and quantitative measurements of the velocity field by a laser Doppler anemometer. Measurements were done for two ranges of Reynolds numbers; about 60 and about 350. The stream function-vorticity form of the governing equations was approximated by upwind or central finite-differences. Both types of finite-difference approximations were solved by a multi-grid method. Numerical solutions were computed on a sequence of grids and the relative accuracy of the solutions was studied. Our most accurate numerical solutions had an estimated error of 0.1 per cent and 1 per cent for Re = 60 and Re = 350, respectively. It was also noted that the solution to the second order finite difference equations was more accurate, compared to the solution to the first order equations, only if fine enough meshes were used. The possibility of using extrapolations to improve accuracy was also considered. Extrapolated solutions were found to be valid only if solutions computed on fine enough meshes were used. The numerical and the experimental results were found to be in very good agreement.
    Additional Material: 22 Ill.
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  • 13
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 347-356 
    ISSN: 0271-2091
    Keywords: Aerofoils ; Unsteady ; Potential ; Discrete ; Vortex ; Two-dimensional ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new model is presented for the calculation of the incompressible, inviscid flow around an arbitrary aerofoil undergoing unsteady motion. The technique was developed from the steady flow algorithm of Leishman and Galbraith1 in which use was made of a linear distribution of panel vorticity. The procedure is in the same class as that of Basu and Hancock2 but, because of the particular approach to the manner of specifying the shed vorticity, only a set of linear simultaneous equations needs be solved, unlike the method of Reference 2, complicated by the necessary solution of a quadratic.A brief history of unsteady flow modelling is given in the introduction, followed by the mathematical details of the current method. Results are presented and discussed for a number of cases which clearly illustrate relevant characteristics of unsteady flow.
    Additional Material: 6 Ill.
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  • 14
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 357-380 
    ISSN: 0271-2091
    Keywords: Iterative Methods ; Implicit Procedures ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A general implicit (GI) method for solving iteratively the algebraic system arising from a finite difference approximation of an elliptic partial differential equation is formulated. Under certain assumptions this method can be reduced to the already known implicit techniques. It is shown that the GI method has a very special physical meaning when solving fluid flow problems. It is shown also how this method can be optimized to achieve the maximum rate of convergence. Finally it is shown how this new strategy is applied by solving some classical numerical fluid dynamics problems.
    Additional Material: 21 Ill.
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  • 15
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 399-401 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 16
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 381-391 
    ISSN: 0271-2091
    Keywords: Matrix Iterative Methods ; Strongly Implicit Procedure ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new method for solving elliptic difference equations is derived based on the strongly implicit method. This parametrized strongly implicit method has three free parameters which may be functions of the field's nodal point. The method has some resemblance to the SOR techniques, but in the present method the off-diagonal entries are also over-relaxed. The main application of this method is for transport equations such as those governing the fluid flow and heat transfer fields.
    Additional Material: 5 Ill.
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  • 17
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 393-397 
    ISSN: 0271-2091
    Keywords: Shallow-Water Equations ; Spurious Solutions ; Numerical Boundary Condition ; Advection ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A simple explanation is given of the occurrence of wiggles in the flow field near outflow boundaries. If the shallow-water equations are solved numerically spurious solutions with an oscillatory character turn out to exist, which can be generated by certain additional numerical boundary conditions on the downstream side. The wiggles usually damp quickly with the distance from the boundary. Some ways of handling the downstream boundary are given which largely avoid the occurrence of wiggles.
    Additional Material: 1 Ill.
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  • 18
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 402-403 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 19
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 20
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 439-442 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Additional Material: 2 Ill.
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  • 21
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 405-425 
    ISSN: 0271-2091
    Keywords: DuFort-Frankel ; Saul'ev ; Instability ; Sea Model ; Hydrodynamic ; Three-dimensional Time-splitting ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A three dimensional hydrodynamic sea model of an arbitrary sea area is formulated using sigma co-ordinates in the vertical. The solution of the equations using finite difference grids in the horizontal and the vertical is described.Discretization of the vertical viscosity term in the hydrodynamic equations using the DuFort-Frankel and Saul'ev methods is developed. Some numerical instabilities occur with the DuFort-Frankel method which can be overcome by splitting the hydrodynamic equations into equations describing the mean flow and equations describing the deviations from it. The computational advantages of solving these equations with different time steps are discussed.The accuracy and stability of the various methods is demonstrated for wind induced flow in a simple rectangular basin having dimensions representing the North Sea.
    Additional Material: 4 Ill.
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  • 22
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 443-462 
    ISSN: 0271-2091
    Keywords: Turbulent flow ; Boundary Layer Flow ; Swirl ; Surface Mass Transfer ; Finite Element Method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The Dorodnitsyn finite element method for turbulent boundary layer flow with surface mass transfer is extended to include axisymmetric swirling internal boundary layer flow. Turbulence effects are represented by the two-layer eddy viscosity model of Cebeci and Smith1 with extensions to allow for the effect of swirl. The method is applied to duct entry flow and a 10 degree included-angle conical diffuser, and produces results in close agreement with experimental measurements with only 11 grid points across the boundary layer. The introduction of swirl (we/ue = 0.4) is found to have little effect on the axial skin friction in either a slightly favourable or adverse pressure gradient, but does cause an increase in the displacement area for an adverse pressure gradient. Surface mass transfer (blowing or suction) causes a substantial reduction (blowing) in axial skin friction and an increase in the displacement area. Both suction and the adverse pressure gradient have little influence on the circumferential velocity and shear stress components. Consequently in an adverse pressure gradient the flow direction adjacent to the wall is expected to approach the circumferential direction at some downstream location.
    Additional Material: 15 Ill.
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  • 23
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 463-481 
    ISSN: 0271-2091
    Keywords: Trailing-edge Flow ; Laminar Flow ; Turbulent Flow ; Generalized Co-ordinates ; Group Finite-element Method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A consistent three-level time-split group finite-element method, suitable for the computation of viscous compressible flows in irregular geometric domains, is described. Exploitation of the group12 formulation permits an accurate and economical algorithm to be developed in a generalized-co-ordinate (ζ,η) space. A variable sweep cycle is used to accelerate convergence to the steady state. The method is demonstrated by computing laminar and turbulent flow past a trailing edge. The method uses an algebraic eddy viscosity model to represent turbulence and produces results in close agreement with the experiments and computations of Viswanath et al8.
    Additional Material: 12 Ill.
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  • 24
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 427-438 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The problem under investigation is that of fluid flow within an enclosed rectangular cavity. It is assumed that one wall is maintained at a constant temperature T1 (hot wall) and the other wall is maintained at a constant temperature T0 (cold wall). At the remaining walls, two separate cases are studied. In the first, an adiabatic boundary condition is assumed. That is, the normal derivative of the temperature function is assumed to be 0. In the second, it is assumed the temperature varies linearly from T0 to T1.The purpose of this paper is the application of a second order numerical technique to the problem of fluid flow within a heated closed cavity. The method is a modification of a method developed by Shay1 and applied to the driven cavity problem. In order to test the viability of this technique, it was decided to extend the technique to the problem of natural convection in a square. Jones2 proposed that this problem is suitable for testing techniques that may be applied to a wide range of practical problems such as reactor insulation, cooling of radioactive waste containers, solar energy collection and others.3The technique makes use of second-order finite difference approximations to all derivatives in the governing equations. Furthermore, second-order approximations are also used to determine boundary vorticities and, when the adiabatic boundary condition is used, for the boundary temperatures as well. In some works, where second-order approximations are used at interior points, second-order boundary approximations have been sacrificed in favour of a more stable, but first-order boundary approximation.The current approximations are generated by writing the unknown value of a function at a given interior node as a linear combination of unknown function values at all of the neighbouring nodes. Then the function values at these neighbouring nodes are expanded in a Taylor series about the given node. Through appropriate regrouping of terms and the use of the equations to the solved, constraints are imposed on the coefficients of the linear combination to yield a second-order approximation. As it turns out, there are more unknowns than constraints and, as a result, we are left with some freedom in choosing coefficients. In this work this freedom was used to choose coefficients in such a way as to maximize stability of the resulting system of equations. In other words, the approximations to the governing partial differential equation are individually determined at each point dependent on the direction of flow in order to generate the best possible stability. This idea is analogous to that used in the derivation of the upwind method. However, the current method is second-order accurate where the upwind method is only first-order accurate. Thus, what is generated is an easily implemented second-order method that yields a system of equations that has proved easy to solve.The system of equations is solved via the method of successive overrelaxation. The stability of the method is shown in the convergence for a wide range of Rayleigh numbers, Prandtl numbers and mesh sizes. Level curves of the stream, vorticity and temperature functions are provided for Rayleigh numbers (Ra) as large as 100,000, Prandtl numbers (Pr) as small as 0.0001, and mesh sizes as small as 0.0125. Values of the Nusselt number have also been calculated through the use of Simpson's rule, and a second order approximation to the normal derivative of the temperature along the cold wall. Comparisons are made with other current works to aid in the verification of this methods' accuracy and also with the first-order upwind method to demonstrate superiority over the first-order method.
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  • 25
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 483-500 
    ISSN: 0271-2091
    Keywords: Three-dimensional Vortex flow ; Pseudo-unsteady Euler Equations ; Finite Volume ; Multiple Grid ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The unsteady Euler equations are numerically solved using the finite volume one-step scheme recently developed by Ron-Ho Ni. The multiple-grid procedure of Ni is also implemented. The flows are assumed to be homo-enthalpic; the energy equation is eliminated and the static pressure is determined by the steady Bernoulli equation; a local time-step technique is used. Inflow and outflow boundaries are treated with the compatibility relations method of ONERA. The efficiency of the multiple-grid scheme is demonstrated by a two-dimensional calculation (transonic flow past the NACA 12 aerofoil) and also by a three-dimensional one (transonic lifting flow past the M6 wing). The third application presented shows the ability of the method to compute the vortical flow around a delta wing with leading-edge separation. No condition is applied at the leading-edge; the vortex sheets are captured in the same sense as shock waves. Results indicate that the Euler equations method is well suited for the prediction of flows with shock waves and contact discontinuities, the multiple-grid procedure allowing a substantial reduction of the computational time.
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  • 26
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    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 501-501 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 27
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 502-503 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 28
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    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 29
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 505-513 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Computational difficulties arise in the non-linear free-surface problem for water waves both at large amplitudes when the crest becomes nearly singular and at small amplitudes when the wave is very close to the alternative uniform flow solution. Since the limiting wavelengths for small amplitude waves are known from the Stokes linearized theory, these are used in checking results for finite-amplitude programs. When Southwell and Vaisey1 first tried this, their methods gave an unexplained overestimate, by 6 per cent, of the limiting wavelength. This paper shows how coarse mesh effects can create such an overestimate, gives very accurate solutions at small amplitudes and considers accuracy in relation to the mesh for short and long waves.
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  • 30
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 515-528 
    ISSN: 0271-2091
    Keywords: Solution Adaptive ; Grids (SAG) ; Mesh Generation ; Techniques ; Burgers Equation ; Falkner-Skan Equation ; Viscous Aerofoil Flows ; Navier-Stokes Equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A solution adaptive grid (SAG) method which redistributes the nodal points of a function according to its curvature is presented. A single, user-selected step parameter, P, is available for controlling the maximum step size, allowing the application of the technique to a wide variety of problems. Three test cases are cited: (1) the 1-dimensional inviscid Burgers equation, (2) the Falkner-Skan equation and (3) the finite-volume form of the Navier-Stokes equations for transonic aerofoil flows. In all three cases, significant solution improvement in terms of accuracy and convergence acceleration were achieved.
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  • 31
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 529-543 
    ISSN: 0271-2091
    Keywords: Shallow Water Equations ; Analytic Solutions ; Three-dimensional ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Exact periodic solutions are generated for the 3-D hydrodynamic equations in linearized form. A linear slip condition is enforced at the bottom, based on the velocity at the bottom. It is shown that the bottom stress can be equivalently expressed in terms of the vertically averaged velocity, and expressions for this bottom stress coefficient are derived in terms of the primary parameters of the problem. As a result, the three-dimensional structure may be assembled from conventional solutions to (a) the 1-D vertical diffusion equation; and (b) the 2-D vertically averaged shallow water equations. In the latter, the bottom stress effects are shown to be complex and frequency-dependent, and an additional rotational term is required for their representation.
    Additional Material: 5 Ill.
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  • 32
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 593-596 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this note we show that the numerical solution of the advection-diffusion equation can be improved by considering the asymptotic behaviour of its analytical solution. This is accomplished by including a correction term based on the numerical differentiation of the asymptotic (Pe » 1, Pe being the Peclet number) solution. This correction forces the usual oscillations associated with centred schemes to disappear.
    Additional Material: 1 Ill.
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  • 33
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 545-560 
    ISSN: 0271-2091
    Keywords: Boundary Layer Flows ; Time-like ; Co-ordinate ; Space-like ; Domain ; Inviscid ; Tangential ; Velocity ; Pressure Gradient ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical procedure was developed to solve the two-dimensional and axisymmetric incompressible laminar boundary layer equations using the semi-discrete Galerkin finite element method. Linear Lagrangian, quadratic Lagrangian, and cubic Hermite interpolating polynomials were used for the finite element discretization; the first-order, the second-order backward difference approximation, and the Crank-Nicolson method were used for the system of non-linear ordinary differential equations; the Picard iteration and the Newton-Raphson technique were used to solve the resulting non-linear algebraic system of equations. Conservation of mass is treated as a constraint condition in the procedure; hence, it is integrated numerically along the solution line while marching along the time-like co-ordinate. Among the numerical schemes tested, the Picard iteration technique used with the quadratic Lagrangian polynomials and the second-order backward difference approximation case turned out to be the most efficient to achieve the same accuracy. The advantages of the method developed lie in its coarse grid accuracy, global computational efficiency, and wide applicability to most situations that may arise in incompressible laminar boundary layer flows.
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  • 34
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 561-575 
    ISSN: 0271-2091
    Keywords: Cavity Flow ; Incompressible Flow ; Control-Volume Formulation ; Navier-Stokes Equations ; QUICK ; Convection Scheme ; Taylor-Görtler Vortices ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Previous three-dimensional simulations of the lid-driven cavity flow have reproduced only the most general features of the flow. Improvements to a finite difference code, REBUFFS, have made possible the first completely successful simulation of the three-dimensional lid-driven cavity flow. The principal improvement to the code was the incorporation of a modified QUICK scheme, a higher-order upwind finite difference formulation. Results for a cavity flow at a Reynolds number of 3200 have reproduced experimentally observed Taylor-Görtler-like vortices and other three-dimensional effects heretofore not simulated. Experimental results obtained from a unique experimental cavity facility validate the calculated results.
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  • 35
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 577-592 
    ISSN: 0271-2091
    Keywords: Unsteady ; Separation ; Discrete Vortex ; Aerofoil ; Wake ; Inviscid ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Presented in this paper is a new method for the prediction of unsteady, incompressible separated flow over a two-dimensional aerofoil. The algorithm was developed from an existing unsteady potential flow model1 and makes use of an inviscid formulation for the flow field. The aerofoil is represented by vortex panels of linearly varying strength which are piecewise continuous at the corners. Discrete vortices with finite cores are used to model the separating shear layers.Following a brief summary of unsteady separation modelling, the theoretical framework is presented and the subsequent numerical implementation is discussed in detail.Results are given for flows which tend asymptotically to the steady state and conclusions are drawn regarding the usefulness of the method.
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  • 36
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 597-598 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 37
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 599-600 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 38
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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 39
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 601-614 
    ISSN: 0271-2091
    Keywords: Finite Elements ; Stokes Equations ; Periodically Constricted Tubes ; Quadrilateral Elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The use of the finite element method in solving the problem of flow of a Newtonian fluid in periodically constricted tubes is explored. The performance of eight node serendipity and nine node Lagrangian elements is compared. It was found that the Lagrangian element results in unstable velocity fields when stagnant or recirculation regions are present. This is characteristic of tubes with large expansion zones. The eight node element does not exhibit instabilities. Both elements give accurate pressure fields. This behaviour is contrary to traditional results obtained for flow problems with similar geometrical characteristics. This suggests that the periodicity of the boundary conditions might be the cause of the instabilities in the numerical solution.The use of the continuity equation to simplify the viscous terms in the Stokes equations resulted, in this particular case, in a deterioration of the rate of convergence of the algorithm.
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  • 40
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 627-635 
    ISSN: 0271-2091
    Keywords: Pressure Gradient Method ; Unsteady Flow ; Cavity Flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The pressure gradient method using velocity components and components of a pressure gradient as dependent variables has been modified to solve incompressible Newtonian fluid flow problems numerically. Applying this modified method to unsteady-state development of flow in a circular cavity shows that, at least for the case of a low Reynolds number flow, relative errors produced by the proposed method are smaller for most time intervals than those produced by the primitive velocity-pressure variable method and by the standard pressure gradient method. Also it is found that the modified and standard pressure gradient methods can be applied to the unsteady circular cavity flow at a moderate Reynolds number of at least up to 200.
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  • 41
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 637-656 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper presents finite element methods for the non-stationary Euler equations of a two dimensional inviscid and incompressible flow. For the time discretization, we compare numerical results obtained by the use of a leap-frog scheme and a semi-implicit scheme of order two.
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  • 42
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 615-625 
    ISSN: 0271-2091
    Keywords: Incompressible Flow ; Coupled Line Gauss Seidel ; Two Dimensional ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper describes an iterative technique for solving the coupled algebraic equations for mass and momentum conservation for an incompressible fluid flow. The technique is based on the simultaneous solution for pressure and velocity along lines. In a manner similar to ADI methods for a single variable, the solution domain is entirely swept line-by-line in each co-ordinate direction successively until a converged solution is obtained. The tight coupling between the equations that is guaranteed by the method results in an economical solution of the equation set.
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  • 43
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 657-663 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 44
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 664-664 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 45
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 665-666 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 46
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 666-666 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 47
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    International Journal for Numerical Methods in Fluids 5 (1985) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 48
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 667-683 
    ISSN: 0271-2091
    Keywords: Laminar Flows ; Complex Geometry ; Numerical Methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper reports on the outcome of a workshop of the IAHR Working Group on Refined Modelling of Flows on the subject of computing laminar flows in complex geometries. Flow inside a channel with a smooth expansion was chosen by the organizers of the workshop as a suitable test case for assessing the capabilities of current numerical methods. The results obtained by fifteen participant groups are presented and compared against a suitable benchmark solution. The most important considerations that emerged at the workshop are briefly reported and the conclusions arising from an analysis and comparison of the various solutions are finally provided.
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  • 49
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 685-707 
    ISSN: 0271-2091
    Keywords: Navier-Stokes Problem ; Monochromatic Dynamic Behaviour ; Uzawa Algorithm ; Darcy's Law ; Conforming Finite Element Methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper computations in the two dimensional case of a harmonic Navier-Stokes problem with periodic boundary conditions are presented. This study of an incompressible viscous fluid leads to a non-symmetric linear problem (very low Reynolds number). Moreover unknown functions have complex values (monochromatic dynamic behaviour). Numerical treatment of the incompressibility condition is a generalization of the classical treatment of Stokes problem. A mixed formulation, where discrete pressure plays the role of Lagrange multipliers is used (Uzawa algorithm).Two conforming finite element methods are tested on different meshes. The second one uses a classical refinement in the shape function: the so-called bulb function. All computational tests show that the use of a bulb function on each element gives better results than refinement in the mesh without introducing too many degrees of freedom. Finally numerical results are compared to experimental data.
    Additional Material: 23 Ill.
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  • 50
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 709-725 
    ISSN: 0271-2091
    Keywords: Isothermal Laminar Flow ; Finite Elements ; Flow Past a Sphere ; Surface Blowing ; Drag ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Steady, axisymmetric, isothermal, incompressible flow past a sphere with uniform blowing out of the surface is investigated for Reynolds numbers in the range 1 to 100 and surface velocities up to 10 times the free stream value. A stream-function-velocity formulation of the flow equations in spherical polar co-ordinates is used and the equations are solved by a Galerkin finite-element method. Reductions in the drag coefficients arising from blowing are computed and the effects on the viscous and pressure contributions to the drag considered. Changes in the surface pressure, surface vorticity and flow patterns for two values of the Reynolds number (1 and 40) are examined in greater detail. Particular attention is paid to the perturbation to the flow field far from the sphere.
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  • 51
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 745-760 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Dynamic and thermal results for developing laminar pulsed flows in a duct are presented. They have been investigated by means of a finite difference model. This flow is described in terms of an unsteady pulsed flow superimposed on a steady incompressible one with the following main assumptions: a sinusoidal modulation for the pulsation and a uniform wall temperature. Results emphasize the importance of this entry region, where four simultaneous developments occur: steady - dynamic and thermal - and unsteady - dynamic and thermal.
    Additional Material: 16 Ill.
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  • 52
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 727-744 
    ISSN: 0271-2091
    Keywords: Shallow Water Equations ; Boundary Fitted Grids ; Comparison of Boundary Fitted Grid Model with x-y Cartesian Grid Model ; Annular Ring Solutions ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Many problems of applied oceanography and environmental science demand the solution of the momentum, mass and energy equations on physical domains having curving coastlines. Finite-difference calculations representing the boundary as a step function may give inaccurate results near the coastline where simulation results are of greatest interest for numerous applications. This suggests the use of methods which are capable of handling the problem of boundary curvature.This paper presents computational results for the shallow water equations on a circular ring of constant depth, employing the concept of boundary fitted grids (BFG) for an accurate representation of the boundary. All calculations are performed on a rectangle in the transformed plane using a mesh with square grid spacing. Comparisons of the simulations of transient normal mode oscillations and analytic solutions are shown, demonstrating that this technique yields accurate results in situations (provided that there is a reasonable choice of grid) involving a curved boundary. The software developed allows application to any two-dimensional area, regardless of the complexity of the geometry.Simulation runs were made with two co-ordinate systems. For the first system, the grid point distribution was obtained from polar co-ordinates. For the second one, grid point positions were calculated numerically, solving Poisson's equation. It was found that small variations in the metric coefficients do not deteriorate the accuracy of the simulation results.Moreover, comparisons of surface elevation and velocity components at grid points near the inner and outer radii obtained from an x-y Cartesian grid model with the BFG simulation were made. The former model produced inacccuracies at grid points near boundaries, and, owing to the large number of mesh points used to yield the necessary fine resolution, the computation time was found to be a factor of three higher.
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  • 53
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 761-762 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 54
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 762-762 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 55
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    International Journal for Numerical Methods in Fluids 5 (1985) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 56
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 763-783 
    ISSN: 0271-2091
    Keywords: Solenoidal Vector Fields ; Fast Poisson Solvers ; Boundary Integral Methods ; Far Field Approximations ; Navier-Stokes Equations ; Capacitance Matrices ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We develop a new method for the efficient calculation of solenoidal vector fields on general regions. The method takes advantage of fast direct methods and uses boundary integral equations to satisfy boundary conditions. For the latter we give an effective scheme for computing far-field boundary influences (based on discrete charges). Examples and numerical results are given. The method is applicable to incompressible Navier-Stokes calculations.
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  • 57
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 805-816 
    ISSN: 0271-2091
    Keywords: Diffusion-Convection ; Finite Element Method ; Hermite Interpolation Function ; Numerical Analysis ; Stability ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The paper is concerned with stability and accuracy of an nth order Lagrangian family of finite element steady-state solutions of the diffusion-convection equation, and furthermore is concerned with the stability and the accuracy of on mth kind Hermitian family of finite element solutions. We discuss the stability of the numerical solution based on the fact that the characteristic finite element solution can be expressed approximately as a rational function of cell Peclet number Pec ( = uh/k). Moreover, it is shown that by eliminating derivatives and by using the interpolation method over elements a stable solution is obtained over the domain independent of Pec for P1,3, and for P2,5 the stable solution is obtained for Pec less than 44.4.
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  • 58
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 785-803 
    ISSN: 0271-2091
    Keywords: Variable Penalty Method ; Penalty Finite Element Analysis ; Rotating Flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A new scheme is applied for increasing the accuracy of the penalty finite element method for incompressible flow by systematically varying from element to element the sign and magnitude of the penalty parameter λ, which enters through ∇.v + p/λ = 0, an approximation to the incompressibility constraint. Not only is the error in this approximation reduced beyond that achievable with a constant λ, but also digital truncation error is lowered when it is aggravated by large variations in element size, a critical problem when the discretization must resolve thin boundary layers. The magnitude of the penalty parameter can be chosen smaller than when λ is constant, which also reduces digital truncation error; hence a shorter word-length computer is more likely to succeed. Error estimates of the method are reviewed. Boundary conditions which circumvent the hazards of aphysical pressure modes are catalogued for the finite element basis set chosen here. In order to compare performance, the variable penalty method is pitted against the conventional penalty method with constant λ in several Stokes flow case studies.
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  • 59
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 817-830 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The problem of computing the vibration modes of a structure vibrating in a fluid is examined with specific application to ship hulls. In particular, methods which take proper account of the three-dimensional nature of the water movements are described. Fluid singularities involving either a line doublet on the intersection of the water surface with the plane of symmetry or distributed sources on retracted boundaries are particularly effective at modelling the fluid flow and appear to give better numerical efficiencies than finite element or boundary element methods. The effects of the extra coefficients in the mass matrix arising from added mass on the various methods of eigensolution are discussed.
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  • 60
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 847-848 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 61
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    International Journal for Numerical Methods in Fluids 5 (1985) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 62
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 831-845 
    ISSN: 0271-2091
    Keywords: Non-Newtonian ; Finite Element Method ; Optimal Control ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Modern lubricants often exhibit shear-thinning due to the presence of high molecular weight polymers as additives. Therefore the influence of such non-Newtonian effects on the performances of lubricating systems must be predicted. The corresponding fluid film flow is governed by a non-linear partial differential equation, which generalizes the classical Reynolds equation. Having prescribed adequate boundary conditions, this equation is solved by a finite element method with optimal control. The problem of the square slider bearing lubricated by the Rabinowitsch fluid is solved in order to test the accuracy of the numerical scheme. The pressure and velocity fields are given and compared with the corresponding ones obtained for the Newtonian fluid.
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  • 63
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 849-871 
    ISSN: 0271-2091
    Keywords: Random Vortex Method ; Wind Engineering ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The random vortex method of Chorin1 provides a numerical simulation of high-Reynolds number flow in two dimensions. The method can be used to model the viscous interaction of wind with a surface-mounted obstacle of arbitrary cross-section. In this paper the method has been used to investigate the flow of wind over common building shapes; an inlet profile is chosen to represent the stationary aspects of the atmospheric boundary layer. The evolution of flow over a short time-interval after flow initialization is depicted, and a mean value of pressure coefficient, Cp, is calculated over the building perimeter. Some comparison is made with published wind-tunnel measurements for the case of a surface-mounted square-section block and for a building model with 10° roof pitch.
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  • 64
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 911-928 
    ISSN: 0271-2091
    Keywords: Incompressible ; Finite Elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We present a numerical procedure to eliminate internal nodes from elements designed to approximate incompressible flow problems. We compare six elements in academic and industrial like flow problem and we discuss their relative qualities. A surprising conclusion is that richer elements may behave less well than simple ones if a good enforcement of incompressibility is not maintained.
    Additional Material: 15 Ill.
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  • 65
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 891-909 
    ISSN: 0271-2091
    Keywords: Green's Functions ; Boundary Element Method ; Waves ; Special Functions ; Series ; Convergence ; Acceleration ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We have studied the problem of calculating Green's functions in three dimensional hydrodynamic gravity wave problems. A number of new expressions for these functions are presented for both finite and infinite depths. Various techniques for accelerating the convergence of some infinite series in these expressions are investigated and compared with the normal methods of evaluation. A significant improvement in the efficiency of the calculation is found using the results described in this paper.
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  • 66
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 873-890 
    ISSN: 0271-2091
    Keywords: Incompressible Navier-Stokes Equations ; Finite Element Method ; Direct Time ; Integration Method ; Vortex Shedding Behind an Obstacle ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical procedure for solving the time-dependent, incompressible Navier-Stokes equations is presented. The present method is based on a set of finite element equations of the primitive variable formulation, and a direct time integration method which has unique features in its formulation as well as in its evaluation of the contribution of external functions. Particular processes regarding the continuity conditions and the boundary conditions lead to a set of non-linear recurrence equations which represent evolution of the velocities and the pressures under the incompressibility constraint. An iteration process as to the non-linear convective terms is performed until the convergence is achieved in every integration step. Excessively artificial techniques are not introduced into the present solution procedure. Numerical examples with vortex shedding behind a rectangular cylinder are presented to illustrate the features of the proposed method. The calculated results are compared with experimental data and visualized flow fields in literature.
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  • 67
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 939-939 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 68
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    International Journal for Numerical Methods in Fluids 5 (1985) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 69
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 940-941 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 70
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 929-938 
    ISSN: 0271-2091
    Keywords: Non-Newtonian Fluid Flow ; Nine-Node Lagrangian Element ; Broyden's Method ; Frontal Method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: When the Galerkin finite-element method with a nine-node isoparametric Lagrangian element is applied to solve non-Newtonian fluid flow problems, a considerable amount of computing time is required to solve the discretized non-linear system of equations by Newton's method. A method proposed by Broyden has been modified to compute the Jacobian matrix associated with Newton's method. This modified Broyden's method can be combined with the frontal method to efficiently solve the linearized finite-element equations during the iteration. Numerical results of a sample problem concerning the determination of the pressure-drop/flow-rate relationship for power-law fluids in rectangular ducts show that the application of this new method can reduce computing time substantially.
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  • 71
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 943-955 
    ISSN: 0271-2091
    Keywords: Finite Element ; Reservoir ; Hydrostatic Pressure ; Numerical Accuracy ; Stratified Flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Experiences relating to the application of finite element models for laterally averaged stratified flow are discussed and modifications to the basic approach are suggested that alleviate these difficulties. An example problem is used to demonstrate the revised model and to make a preliminary assessment of the hydrostatic pressure assumption when applied to reservoir analysis.
    Additional Material: 6 Ill.
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  • 72
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 957-980 
    ISSN: 0271-2091
    Keywords: Gas-liquid Flows ; Laminar Boundary Layers ; Heat and Mass Transfer ; Numerical Methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The two-dimensional, laminar boundary-layer equations of heat, mass and momentum at a smooth, phase-changing, gas-liquid interface are solved numerically by the Keller Box method. The gas and liquid regimes are embedded in a single marching scheme which computes interfacial parameters implicitly. Results of both self-similar and non-similar boundary-layer computations are presented and effects of mild pressure gradient, a mean current in the liquid, and free-stream vapour concentration on the interfacial parameters are analysed.In order to assess the accuracy of the method, several self-similar problems are solved by Runge-Kutta integration and results are compared to those obtained by the finite-difference scheme. Agreement is excellent in all cases.
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  • 73
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 981-993 
    ISSN: 0271-2091
    Keywords: Finite Element Method ; Velocity Correlation Method ; Density Flow ; Density Flume ; Linear Interpolation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite element method is proposed for the analysis of density flow which is induced by a difference of density. The method employs the idea that density variation can be pursued by using markers distributed in the flow field. For the numerical integration scheme, the velocity correction method is successfully used, introducing a potential for the correction of velocity. This method is useful because one can use linear interpolation functions for velocity, pressure and potential based on the triangular finite element. The final equations can be formulated using the quasi-explicit finite element method. A flume in a tank with sloping bottom has been analysed by the present method. The computed results show extremely good agreement with the experimental observations.
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  • 74
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 995-1013 
    ISSN: 0271-2091
    Keywords: Boussinesq Approximation ; Porous Media ; Finite Element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The regions of applicability of the Boussinesq approximation are investigated for natural convection in a fluid-saturated porous medium. A perturbation method is used to assess the relative importance of individual terms in the differential equations which describe the natural convection process. Specific limits to the validity of the Boussinesq approximation are identified for water and air. For water, it is shown that the restrictions imposed by the classical Boussinesq approximation can be relaxed by allowing for the variation of thermophysical properties with temperature while still retaining the incompressible form of the continuity relation. Results of the analysis are verified through numerical calculations performed for steady natural convection in a planar, water-saturated porous region.
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  • 75
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 1015-1015 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 76
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    International Journal for Numerical Methods in Fluids 5 (1985) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 77
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 1059-1060 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 78
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 1017-1034 
    ISSN: 0271-2091
    Keywords: Vorticity-Velocity ; Numerical Method ; Coupled Solution ; Block Tridiagonal Matrix ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A relatively novel formulation of the Navier-Stokes equations is used for obtaining solutions of two dimensional incompressible fluid flow and convective heat transfer problems. A vorticity transport equation along with two Poisson equations for the velocity components and the energy equation are solved by a finite difference scheme. A coupled solution procedure is used for solving simultaneously the dependent variables along a line, using a block tridiagonal matrix algorithm. The formulation is found to be stable and has features that may be desirable for solving a wide variety of flow and heat transfer problems.
    Additional Material: 15 Ill.
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  • 79
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 1035-1045 
    ISSN: 0271-2091
    Keywords: Laminar Boundary Layer ; Splines ; Incompressible ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An inverse method is presented which accurately determines the pressure distribution for assigned wall shear in a two-dimensional, laminar, incompressible boundary layer. The method reformulates the mechul function scheme of Cebeci and Keller to produce a stable solution in the marching direction and to increase accuracy in the normal direction. In the reformulation a modified pressure gradient parameter variation in the normal direction is used in conjunction with three-point backward differences for streamwise derivatives and fourth-order accurate splines for normal derivatives. The resulting spline-finite difference equations are solved by Newton-Raphson iteration together with partial pivoting. Numerical solutions are presented for self-similar and non self-similar flows and compared with published results.
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  • 80
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 1047-1057 
    ISSN: 0271-2091
    Keywords: Transonic Flow ; Modified Potential ; Finite Elements ; Non-isentropic Flow ; Conservative Method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The classical potential formulation of inviscid transonic flows is modified to account for non-isentropic effects. The density is determined in terms of the speed as well as the pressure, which in turn is calculated from a second-order mixed-type equation derived via differentiating the momentum equations.The present model differs in general from the exact inviscid Euler equations since the flow is assumed irrotational. On the other hand, since the shocks are not isentropic, they are weaker and are placed further upstream compared to the classical potential solution. Furthermore, the streamline leaving the aerofoil does not necessarily bisect the trailing edge.Results for the present conservative calculations are presented for non-lifting and lifting aerofoils at subsonic and transonic speeds and compared to potential and Euler solutions.
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  • 81
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 1060-1060 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 82
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    International Journal for Numerical Methods in Fluids 5 (1985) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 83
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 1-12 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The influence of free stream direction on mixed (natural and forced) convective heat transfer from a circular cylinder is investigated. The cylinder, which has an isothermal surface, is placed with its axis horizontal and normal to the oncoming flow. The free stream direction varies between the vertically upward (parallel flow) and the vertically downward (contraflow) directions. The investigation is based on the time integration of the unsteady, two-dimensional equations of motion and energy until reaching steady conditions. The study is limited to Reynolds numbers up to Re = 40 and Grashoff numbers of Gr = Re2. The results are compared with the available experimental data and the agreement is satisfactory.
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  • 84
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 25-42 
    ISSN: 0271-2091
    Keywords: Fluid Sloshing ; Equivalent Moment of Inertia ; Partitioned Container ; Finite Differences ; Euler's Equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A 3-D numerical code was developed to solve the irrotational flow of an ideal fluid inside a moving cylindrical container with partitions. The problem is formulated in terms of two Poisson equations, the velocity equation and the pressure equation. These are expressed in terms of finite differences and solved by a procedure of line over relaxation. From the fluid pressure we computed the resultant moment on the container which was then expressed in terms of the equivalent moment of inertia. The code was checked against analytical results of Moiseyev and we found an agreement of 2-5 per cent even for a sparse mesh. We then demonstrated the capability of the code by computing the equivalent moment of inertia for various configurations with full and partial partitions.
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  • 85
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 43-70 
    ISSN: 0271-2091
    Keywords: Finite Element ; Incompressible ; Flow ; Non-Newtonian ; Error Estimate ; Crossed Triangles ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Flows of fluids with single-integral memory functionals are considered. Evaluation of the stress at a material point involves the deformation history of that point, and a dominant computational cost in finite element approximation is the construction of streamlines. It is shown that the simple crossed-triangle macro-element is in many ways an ideal finite element for the difficult non-linear, non-self-adjoint problem. The question as to whether this element produces convergent velocity and pressure solutions is addressed in the light of its failure to satisfy the discrete LBB condition. The effect of the element's ill-disposed (‘spurious’) pressure modes is discussed, and a pressure smoothing scheme is given which gives good results in Newtonian and non-Newtonian flows at various Reynolds and Deborah numbers. As an example of the element's success in modelling such flows, the problem of pressure differences in flows over transverse slots is studied numerically. The results are compared with experimental observations of such flows. The effect of fluid memory on the relation between first normal-stress differences and pressure differences is investigated.
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  • 86
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 199-200 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 87
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    International Journal for Numerical Methods in Fluids 5 (1985), S. i 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 88
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    International Journal for Numerical Methods in Fluids 5 (1985) 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 89
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 201-224 
    ISSN: 0271-2091
    Keywords: Numerical Group Velocity ; Fourier Analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The performances of various numerical schemes used to model hyperbolic/parabolic equations have been studied by the calculation of their numerical group velocities. Numerical experiments conducted with one dimensional linear and quadratic Lagrangian finite elements with a Crank-Nicolson finite differencing in time confirm the results of the analysis. The group velocity analysis supplements the well-known amplitude and phase portraits introduced by Leendertse1 and helps explain the occurrence and behaviour of numerical oscillations in both finite difference and finite element schemes.
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  • 90
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 245-255 
    ISSN: 0271-2091
    Keywords: Orthogonal Body-Fitted Grid ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The procedure proposed is based on the solution by finite difference means of a set of Laplace's equations, by the application of a relaxation method.The curvilinear orthogonal grid so generated is fitted to a 2-D physical domain with closed boundary and the contribution of the present work consists in the arbitrary choice of grid points on two adjacent boundaries, in order to achieve the desired density of grid points where the geometry of the boundaries varies rapidly.The method proposed is rapid and stable. Some characteristic examples are finally presented.
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  • 91
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 225-244 
    ISSN: 0271-2091
    Keywords: Convection-Diffusion ; Differencing Schemes ; Discretization Errors ; False Diffusion ; Upwind Scheme ; Higher Order Schemes ; Accuracy ; Stability ; Computational Cost ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A comparative study of seven discretization schemes for the equations describing convection-diffusion transport phenomena is presented. The (differencing) schemes considered are the conventional central- and upwind-difference schemes, together with the Leonard,1 Leonard upwind1 and Leonard super upwind difference1 schemes. Also tested are the so called locally exact difference scheme2 and the quadratic-upstream difference scheme.3,4 In multidimensional problems errors arise from ‘false-diffusion’ and function approximations. It is asserted that false diffusion is essentially a multidimensional source of error. No mesh constraints are associated with errors in function approximation and discretization. Hence errors associated with discretization only may be investigated via one-dimensional problems. Thus, although the above schemes have been tested for one- and two-dimensional flows with sources, only the former are presented here. For 1D flows, the Leonard super upwind difference scheme and the locally exact scheme are shown to be far superior in accuracy to the others at all Peclet numbers and for most source distributions, for the test cases considered. Furthermore, the latter is shown to be considerably cheaper in computational terms than the former. The stability of the schemes and their CPU time requirements are also discussed.
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  • 92
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 293-297 
    ISSN: 0271-2091
    Keywords: Transport Equation ; Polynomial Initial Conditions ; Convergence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Additional Material: 1 Ill.
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  • 93
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    International Journal for Numerical Methods in Fluids 5 (1985), S. 281-292 
    ISSN: 0271-2091
    Keywords: Finite Elements ; Steady Flow ; Navier-Stokes equations ; Multiplier Methods ; Pseudo-Time-Iteration Method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper a fully explicit finite element method (FEFEM) is presented for solving steady incompressible viscous flow problems. This full explicitness is achieved by combining the multiplier (or augmented Lagrangian) method with a pseudo-time-iteration method. FEFEM needs no global matrix at all and is of great advantage to large-scale problems because they can be solved within the limit of core memory.The optimum choice of a time increment and a penalty parameter is discussed and the driven cavity flow at a Reynolds number of 1000 is computed with a refined mesh (60 × 60 elements).
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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  • 94
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 257-268 
    ISSN: 0271-2091
    Keywords: Turbulence Model ; Finite Difference ; QUICK ; Free Surface Flow ; Channel Expansion ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An application of the depth-integrated k-∊ turbulence model is presented for separated flow in a wide, shallow, rectangular channel with an abrupt expansion in width. The well-known numerical problems associated with the use of upwind and central finite differences for convection are overcome by the adoption of the spatially third-order accurate QUICK finite difference technique. Results show that modification of the depth-integrated k-∊ turbulence closure model for streamline curvature leads to significant improvement in the agreement between model predictions and experimental measurements.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
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  • 95
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 269-280 
    ISSN: 0271-2091
    Keywords: Navier-Stokes Equations ; Finite Element Method ; Solenoidal Approach ; Penalty Function Approach ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In this paper the integrated solution approach, the penalty function approach and the solenoidal approach for the finite element solution of the stationary Navier-Stokes equations are compared. It is shown that both the penalty function approach and the solenoidal approach compare favourably to the integrated solution method. For fine meshes the solenoidal approach appears to be the cheapest method.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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  • 96
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 303-304 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 97
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 304-305 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
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  • 98
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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  • 99
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 299-302 
    ISSN: 0271-2091
    Keywords: Compressible ; Fictitious Gas ; Finite Elements ; Error Estimates ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We summarize here some theoretical results for fictitious gas regularization of compressible flow and give error estimates for the finite element approximation to the regularized problem.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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  • 100
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 305-310 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The commonly accepted linear stability analysis for the forward-time centred-space (FTCS) algorithm applied to the transport equation has led to the concept of a cell Reynolds number restriction on the spatial grid size. This paper shows where the commonly accepted original analysis is in error and presents the correct stability restrictions, which are restrictions on the time step, not the spatial grid size. There is no cell Reynolds number restriction. The results are confirmed by numerical computations for the two-dimensional driven cavity problem.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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