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  • 1
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 275-287 
    ISSN: 0271-2091
    Keywords: Curved pipe flow ; Entrance flow ; Finite element method ; Penalty function method ; Experimental validation ; 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 standard Galerkin finite element penalty function method is used to approximate the solution of the three-dimensional Navier-Stokes equations for steady incompressible Newtonian entrance flow in a 90° curved tube (curvature ratio δ = 1/6) for a triple of Dean numbers (κ = 41, 122 and 204). The computational results for the intermediate Dean number (κ = 122) are compared with the results of laser-Doppler velocity measurements in an equivalent experimental model. For both the axial and secondary velocity components, fair agreement between the computational and experimental results is found.
    Additional Material: 7 Ill.
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989) 
    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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  • 3
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 127-150 
    ISSN: 0271-2091
    Keywords: Iterative solution ; Viscous flow ; Generalized conjugate 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: We consider the use of accelerated gradient-type iterative methods for solution of Newtonian and certain non-Newtonian (power-law and Bingham models) viscous flow problems. The formulations are based on penalty and mixed finite element methods, and such factors as the effect of the penalty parameter, asymmetry, continuation and preconditioning are examined.
    Additional Material: 19 Ill.
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 151-165 
    ISSN: 0271-2091
    Keywords: Numerical analysis ; Fluid flow ; Rotating circular duct ; Finite cell method ; Finite element method ; Swirl ; Inlet boundary conditions ; 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 analysis of the flow pattern in the inlet region of a circular pipe rotating steadily about an axis parallel to its own is presented. Both finite cell and finite element methods are used to analyse the problem and they give qualitatively similar results which show that a swirling fluid motion is induced in the pipe inlet region. The analyses show that the direction of swirl is opposite to that of the pipe rotation when viewed along the flow axis and that its magnitude depends on the speed of pipe rotation and throughflow Reynolds number. Neither numerical analysis predicts the marked upturn in friction factor (or pressure drop) which has been observed experimentally. However, a dependence on the pipe inlet boundary conditions is demonstrated.
    Additional Material: 9 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 185-191 
    ISSN: 0271-2091
    Keywords: Stokes equations ; Boundary elements ; Quadrature ; Triangular co-ordinates ; 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 collocation-type boundary element method based on bilinear B-splines is used for the numerical solution of the Stokes Dirichlet problem in bounded domains D ⊂ R3. The computation of the influence matrix requires the numerical evaluation of weakly singular integrals on the domain boundary if the usual double-layer potential ansatz is chosen. Here mostly standard methods with disjoint grids for collocation and integration are used. We develop a special integration scheme based on triangular co-ordinates near the singularity and show its efficiency compared with the method mentioned above.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 193-212 
    ISSN: 0271-2091
    Keywords: Navier-Stokes ; Staggered grid ; Primitive variable formulation ; 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: Nine finite difference schemes using primitive variables on various grid arrangements were systematically tested on a benchmark problem of two-dimensional incompressible Navier-Stokes flows. The chosen problem is similar to the classical lid-driven cavity flow, but has a known exact solution. Also, it offers the reader an opportunity to thoroughly evaluate accuracies of various conceptual grid arrangements.Compared to the exact solution, the non-staggered grid scheme with higher-order accuracy was found to yield an accuracy significantly better than others. In terms of ‘overall performance’, the so-called 4/1 staggered grid scheme proved to be the best. The simplicity of this scheme is the primary benefit. Furthermore, the scheme can be changed into a non-staggered grid if the pressure is replaced by the pressure gradient as a field variable.Finally, the conventional staggered grid scheme developed by Harlow and Welch also yields relatively high accuracy and demonstrates satisfactory overall performance.
    Additional Material: 5 Ill.
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 251-262 
    ISSN: 0271-2091
    Keywords: Theodorsen's method ; Incompressible flow ; Aerofoil theory ; Thickness ratio ; Camber ratio ; 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: Theodorsen's method for calculating the incompressible potential flow past an aerofoil is viewed afresh. It is found that some simple modifications to the computational process make the computations relatively faster, easier and more accurate. The new modifications are applicable to the analysis of conventional aerofoils with up to moderate thickness and camber ratios. Several examples are presented to show the effectiveness of the modifications.
    Additional Material: 2 Ill.
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  • 8
    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; Euler equations ; Finite element ; Hypersonic laminar-viscous flow ; Time marching ; Shock wave interactions ; 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 upwind finite element technique that uses cell-centred quantities and implicit and/or explicit time marching has been developed for computing hypersonic laminar viscous flows using adaptive triangular grids. The approach is an extension to unstructured grids of the LAURA algorithm due to Gnoffo. A structured grid of quadrilaterals is laid out near a solid surface. For inviscid flows the method is stable at Courant numbers of over 100000. A first-order basic scheme and a higher-order flux-corrected transport (FCT) scheme have been implemented. This technique has been applied to the problem of predicting type III and IV shock wave interactions on a cylinder, with a view to simulating the pressure and heating rate augmentation caused by an impinging shock on the leading edge of a cowl lip of an engine inlet. The predictions of wall pressure and heating rates compare very well with experimental data. The flow features are distinctly captured with a sequence of adaptively generated grids.
    Additional Material: 12 Ill.
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  • 9
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 623-650 
    ISSN: 0271-2091
    Keywords: Numerical analysis ; Wave propagation ; Hyperbolic equations ; Quantum mechanics ; 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 analysis of wave propagation in computing domains where hyperbolic equations are approximated with finite differences has revealed surprising analogies between this subject and quantum mechanics. The first part of this paper consists of a review of the corresponding phenomena and of their description with known results from numerical analysis and wave propagation theory. We then introduce a new formalism, containing a finite difference analogue of the classical Schrodinger equation, which describes the ensemble of those phenomena. The validity of the new formalism is verified by its agreement with known theoretical results in numerical wave propagation (it contains in fact many of those results) as well as with new data obtained in numerical experiments with monochromatic waves which display properties similar to those of Schrödinger's wavefunction for the quantum mechanics description of the equivalent experiments with physical particles. While the results of this paper are derived in the context of wave propagation in computing domains, they remain applicable to similar aspects of wave propagation in other (physical) periodic structures.
    Additional Material: 16 Ill.
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  • 10
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 689-712 
    ISSN: 0271-2091
    Keywords: Rotating spheres ; Viscous flow ; Incompressible fluid ; 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 research reported herein involved the study of the transient motion of a system consisting of an incompressible Newtonian fluid in an annulus between two concentric, rotating, rigid spheres. The primary purpose of the research was to study the use of a numerical method for analysing the transient motion that results from the interaction between the fluid in the annulus and the spheres which are started suddenly by the action of prescribed torques. The problems considered in this research included cases where: (a) one or both spheres rotate with prescribed constant angular velocities and (b) one sphere rotates due to the action of an applied constant or impulsive t̰orque.In this research the coupled solid and fluid equations were solved numerically by employing the finite difference technique. With the approach adopted in this research, only the derivatives with respect to spatial variables were approximated with the use of the finite difference formulae. The steady state problem was also solved as a separate problem (for verification purposes), and the results were compared with those obtained from the solution of the transient problem. Newton's algorithm was employed to solve the algebraic equations which resulted from the steady state problem, and the Adams fourth-order predictor-corrector method was employed to solve the ordinary differential equations for the transient problem. Results were obtained for the streamfunction, circumferential function, angular velocity of the spheres and viscous torques acting on the spheres as a function of time for various values of the system dimensionless parameters.
    Additional Material: 22 Ill.
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  • 11
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 747-761 
    ISSN: 0271-2091
    Keywords: Navier-Stokes solutions ; Shock wave/boundary layer interactions ; Newton's iteration ; Upwind differencings ; Symmetric line relaxation ; 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 objective of the paper is twofold. First we describe an upwind/central differencing method for solving the steady Navier-Stokes equations. The symmetric line relaxation method is used to solve the resulting algebraic system to achieve high computational efficiency. The grid spacings used in the calculations are determined from the triple-deck theory, in terms of Mach and Reynolds numbers and other flow parameters. Thus the accuracy of the numerical solutions is improved by comparing them with experimental, analytical and other computational results. Secondly we proceed to study numerically the shock wave/boundary layer interactions in detail, with special attention given to the flow separation. The concept of free interaction is confirmed. Although the separated region varies with Mach and Reynolds numbers, we find that the transverse velocity component behind the incident shock, which has not been identified heretofore, is also an important parameter. A small change of this quantity is sufficient to eliminate the flow separation entirely.
    Additional Material: 12 Ill.
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  • 12
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 921-941 
    ISSN: 0271-2091
    Keywords: Blade design ; Compressors ; Turbines ; Navier-Stokes ; Quasi-3D and 3D systems ; Through-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 paper describes the basic components of a turbomachinery blade design system in use within Rolls-Royce. A number of modelling aspects of the advanced computational methods in use and under development are reviewed together with areas for future research and development.A quasi-3D blade design system which is used for both compressors and turbines is described covering through-flow and blade-to-blade analysis. Various features of blade-to-blade analysis are discussed including the use of compatible design and analysis modes and coupled boundary layer analysis capable of handling attached and separated flow; examples are included to show capabilities. Advances being made in the development and application of Reynolds-averaged Navier-Stokes models are covered showing capabilities with regard to loss and heat transfer prediction.A fully coupled quasi-3D through-flow and blade-to-blade analysis system is described and results presented to show basic capabilities.The need for 3D flow analysis is discussed and the elements of a 3D blade design system presented showing how this links to the traditional quasi-3D system. Examples are given showing basic capabilities of the methods available and under development.Finally areas for future development are presented indicating the mathematical and numerical modelling problems to be addressed.
    Additional Material: 22 Ill.
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  • 13
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1011-1024 
    ISSN: 0271-2091
    Keywords: Inviscid flow ; TVD difference scheme ; Shock wave ; Expansion wave ; 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 improved treatment for the Harten-Yee and Chakravarthy-Osher TVD numerical flux functions in general co-ordinates is presented. The proposed formulation is demonstrated by a series of numerical experiments for three-dimensional flows around the ONERA-M6 wing. The numerical results indicate that it is important to use a suitable artificial compression parameter in order to obtain more accurate solutions around the leading edge of the wing. The two TVD numerical fluxes give excellent results: they capture the shock wave without numerical oscillations, they capture the rapid expansion around the leading edge sharply, they have self-adjusting mechanisms regarding numerical viscosity and they also have robustness.
    Additional Material: 7 Ill.
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  • 14
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1025-1050 
    ISSN: 0271-2091
    Keywords: Unsteady Navier-Stokes equations ; Direct solution method ; Block Gaussian elimination ; Backstep channel ; Incompressible separated 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 unsteady incompressible Navier-Stokes equations are formulated in terms of vorticity and stream-function in generalized curvilinear orthogonal co-ordinates to facilitate analysis of flow configurations with general geometries. The numerical method developed solves the conservative form of the vorticity transport equation using the alternating direction implicit method, whereas the streamfunction equation is solved by direct block Gaussian elimination. The method is applied to a model problem of flow over a backstep in a doubly infinite channel, using clustered conformal co-ordinates. One-dimensional stretching functions, dependent on the Reynolds number and the asymptotic behaviour of the flow, are used to provide suitable grid distribution in the separation and reattachment regions, as well as in the inflow and outflow regions. The optimum grid distribution selected attempts to honour the multiple length scales of the separated flow model problem. The asymptotic behaviour of the finite differenced transport equation near infinity is examined and the numerical method is carefully developed so as to lead to spatially second-order-accurate wiggle-free solutions, i.e. with minimum dispersive error. Results have been obtained in the entire laminar range for the backstep channel and are in good agreement with the available experimental data for this flow problem, prior to the onset of three-dimensionality in the experiment.
    Additional Material: 10 Ill.
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  • 15
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1073-1086 
    ISSN: 0271-2091
    Keywords: k-∊ turbulence model ; Compressible flow ; Bulk dilatation ; Reciprocating engine 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: This paper is concerned with simulation of the mean flow and turbulence evolution in a model engine and comparison of the behaviour of certain important turbulence parameters, namely the intensity, length scale and dissipation time scale, as predicted by three variants of the k-∊ model developed for application to strongly compressible flows. The predictions pertain to the axisymmetric, disc-chamber, four-stroke, Imperial College model engine operating at 200 rpm and compression ratios of 3·5 and 6·7. The paper analyses the predicted variations of these parameters during the induction, compression and expansion strokes and identifies the versions that produce the most consistent and physically plausible variations. The significance, to the turbulence evolution, of the ratio of the turbulence dissipation time scale to the time scale of compression/expansion is also discussed. It is concluded that on these grounds the Morel-Mansour and El Tahry versions are, and the Watkins version is not, suitable for engine applications.
    Additional Material: 3 Ill.
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  • 16
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1121-1143 
    ISSN: 0271-2091
    Keywords: Turbulence ; High-speed flows ; Unstructured grids ; 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 incorporation of algebraic turbulence models in a solver for the 2D compressible Navier-Stokes equations using triangular grids is described. A practical way to use the Cebeci-Smith model and to modify it in separated regions is proposed. The ability of the model to predict high-speed perfect-gas boundary layers is investigated from a numerical point of view.
    Additional Material: 22 Ill.
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  • 17
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1179-1182 
    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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  • 18
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1195-1206 
    ISSN: 0271-2091
    Keywords: Free boundary problem ; Potential flow ; Wave resistance ; BEM ; 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 numerical method to compute the wave resistance of a body submerged in a free stream of finite and infinite depth is presented. Non-linear effects on the free surface are taken into account by an iterative procedure; the solution is in the form of a single-layer potential. For the 2D problem, results are shown for both the cases of finite and infinite depth of the fluid domain, with special emphasis on the supercritical flow in which the consistency of the scheme is pointed out. The method is also extended to the 3D case of a spheroid submerged in deep water. All the results presented are compared with experimental data and analytical solutions available in the literature.
    Additional Material: 7 Ill.
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  • 19
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1235-1267 
    ISSN: 0271-2091
    Keywords: Pseudospectral ; Non-periodic ; Incompressible 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: The reduction-to-periodicity method using the pseudospectral fast Fourier transform (FFT) technique is applied to the solution of non-periodic problems, including the two-dimensional incompressible Navier-Stokes equations. The accuracy of the method is explored by calculating the derivatives of given functions, one- and two-dimensional convective-diffusive problems, and by comparing the relative errors due to the FFT method with a second-order finite difference (FD) method. Finally, the two-dimensional Navier-Stokes equations are solved by a fractional step procedure using both the FFT and the FD methods for the driven cavity flow and the backward-facing step problems. Comparisons of these solutions provide a realistic assessment of the FFT method.
    Additional Material: 26 Ill.
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  • 20
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1269-1283 
    ISSN: 0271-2091
    Keywords: Euler equations ; Real gases ; Local parametrization of the equation of state ; 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 efficient algorithm is presented for the solution of the Euler equations of gas dynamics with a general convex equation of state. The scheme is based on solving linearized Riemann problems approximately, and in more than one dimension incorporates operator splitting. In particular, only one function evaluation in each computational cell is required by using a local parametrization of the equation of state. The scheme is applied to two standard test problems in gas dynamics for some specimen equations of state.
    Additional Material: 7 Ill.
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  • 21
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1145-1164 
    ISSN: 0271-2091
    Keywords: Riemann problem ; Covolume ; Random choice ; 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 Riemann problem for the unsteady one-dimensional Euler equations together with the constant-covolume equation of state is solved exactly. The solution is then applied to the random choice method to solve the general initial-boundary value problem for the Euler equations. The iterative procedure to find p*, the pressure between the acoustic waves, involves a single algebraic (non-linear) equation, all other quantities follow directly throughout the x-t plane, except within rarefaction fans where an extra iterative procedure is required. The solution is validated against existing exact results both directly and in conjunction with the random choice method.
    Additional Material: 11 Ill.
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  • 22
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989) 
    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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  • 23
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1207-1219 
    ISSN: 0271-2091
    Keywords: Centre implicit method ; Pressure transients ; Two-phase pipe flow ; Bubbly pipe 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: This paper presents a two-dimensional model for the analysis of the pressure transient of a two-phase homogeneous bubbly mixture flowing in a pipeline and the numerical integration using the centre implicit method (CIM). Experiments were conducted to confirm the proposed sonic speed equation of an air-water mixture for an air concentration of less than 1%. The 2D CIM model is compared with the method of characteristics (MoC) for a two-phase bubbly flow in a pipeline. The comparisons show that the proposed 2D CIM model generally gives good agreement with the method of characteristics.
    Additional Material: 7 Ill.
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  • 24
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1299-1301 
    ISSN: 0271-2091
    Keywords: Navier-Stokes equation ; 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 a recent paper a generalized potential flow theory and its application to the solution of the Navier-Stokes equation are developed.1 The purpose of this comment is to show that the analysis presented in that paper is in general not correct. We note that the theoretical development of Reference 1 is in fact an extension - although not cited - of some work first done by Hawthorne for steady inviscid flow.2 Hawthorne's solution is correct, and his analysis, which we briefly describe, provides a useful introduction to this note.
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  • 25
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989) 
    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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  • 26
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1395-1411 
    ISSN: 0271-2091
    Keywords: Reduced Navier-Stokes computations ; Flow separation ; Laminar instability ; 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 convergence properties of an iterative solution technique for the Reduced Navier-Stokes equations are examined for two-dimensional steady subsonic flow over bump and trough geometries. Techniques for decreasing the sensitivity to the initial pressure approximation, for fine meshes in particular, are investigated. They are shown to improve the robustness of the relaxation process and to decrease the computational work required to obtain a converged solution. A semi-coarsening multigrid technique that has previously been found to be particularly advantageous for high-Reynolds-number (Re) flows with flow separation and with highly stretched surface-normal grids is applied herein to further accelerate convergence. Solutions are obtained for the laminar flow over a trough that is more severe than has been considered to date. Sufficient axial grid refinement in this case leads to a shock-like reattachment and, for sufficiently large Re, to a local ‘divergence’ of the numerical computations. This ‘laminar flow breakdown’ appears to be related to an instability associated with high-frequency fine-grid modes that are not resolvable with the present modelling. This behaviour may be indicative of dynamic stall or of incipient transition. The breakdown or instability is shown to be controllable by suitable introduction of transition turbulence models or by laminar flow control, i.e. small amounts of wall suction. This lends further support to the hypothesis that the instability is of a physical rather than numerical character and suggests that full three-dimensional analysis is required to properly capture the flow behaviour. Another inference drawn from this investigation is that there is a need for careful grid refinement studies in high-Re flow computations, since coarser grids may yield oscillation-free solutions that cannot be obtained on finer grids.
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  • 27
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1453-1467 
    ISSN: 0271-2091
    Keywords: Fourier wave theory ; Limit wave ; Stream function ; Truncation order ; 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 review of the analytical and numerical background of Fourier wave theory establishes the commonality of existing formulations and identifies a number of analytical and numerical assumptions that are unnecessary. Some formulations in particular lack flexibility in excluding the possibility of Stokes' second definition of phase speed. A generalized formulation is introduced for comparative purposes and it is shown that published solutions differ only in the approach to the limit wave. Detailed consideration of truncation order confirms that it is the crucial parameter, especially at extreme wave heights. All formulations considered are shown to provide acceptable solutions for small to moderately extreme waves.
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  • 28
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1487-1501 
    ISSN: 0271-2091
    Keywords: Viscoelastic fluid ; Polymer flow ; Velocity correction method ; Two-step explicit scheme ; Pressure boundary condition ; 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 effects of non-Newtonian behaviour of a fluid and unsteadiness on flow in a channel with non-uniform cross-section have been investigated. The rheological behaviour of the fluid is assumed to be described by the constitutive equation of a viscoelastic fluid obeying the Oldroyd-B model. The finite element method is used to analyse the flow. The novel features of the present method are the adoption of the velocity correction technique for the momentum equations and of the two-step explicit scheme for the extra stress equations. This approach makes the computational scheme simple in algorithmic structure, which therefore implies that the present technique is capable of handling large-scale problems. The scheme is completed by the introduction of balancing tensor diffusivity (wherever necessary) in the momentum equations. It is important to mention that the proper boundary condition for pressure (at the outlet) has been developed to solve the pressure Poisson equation, and then the results for velocity, pressure and extra stress fields have been computed for different values of the Weissenberg number, viscosity due to elasticity, etc. Finally, it is pertinent to point out that the present numerical scheme, along with the proper boundary condition for pressure developed here, demonstrates its versatility and suitability for analysing the unsteady flow of viscoelastic fluid through a channel with non-uniform cross-section.
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  • 29
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 23-41 
    ISSN: 0271-2091
    Keywords: Momentum transport ; Turbulent mixing layers ; Discrete vortex method ; Time-dependent momentum fluctuations ; Comparison with experiments ; Large-scale structures ; 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 turbulent momentum transport phenomena in a two-dimensional mixing layer are investigated numerically by a discrete vortex method. The numerical model and calculations are verified through a comparison with existing numerical simulations and experimental measurements. The main emphasis is placed on the exploration of the detailed time-dependent instantaneous local momentum fluctuations and on the comparison of numerical results with available experimental measurements. The current simulations confirm qualitatively the various trends in the turbulent momentum flux and fluctuating components of the velocity in the mixing layer found with several experimental results. The study shows that similarity exists in turbulent momentum quantities along the axial direction of the mixing layer. The calculations also show a definite correlation between the passage of a large-scale structure and a burst in the turbulent momentum flux. The probability density functions of the fluctuating quantities are shown to be mostly Gaussian-like, with only a few exceptions.
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  • 30
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 9-22 
    ISSN: 0271-2091
    Keywords: Shock capturing ; Shock tube ; TVD scheme ; Compressible flow ; Fluid dynamics ; Comparison with experiment ; 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: Harten's second-order-accurate total-variation-diminishing (TVD) scheme is applied to calculation of flow from the open end of a shock tube. Comparison of numerical results with available experimental data for overpressure at selected points around the shock tube exit shows good agreement. Numerically indicated positions of the moving shock front and Mach stem also compare well with flow shadowgraph data. Where the problem geometry is sufficiently simple and rectangular gridding can be used, Harten's method affords a good choice for blast wave calculations.
    Additional Material: 13 Ill.
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  • 31
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 59-73 
    ISSN: 0271-2091
    Keywords: Steady Euler equations ; Transonic flows ; Multigrid methods ; Boundary conditions ; 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 2D Euler flow computations have been performed for a wind tunnel section, designed for research on transonic shock wave-boundary layer interaction. For the discretization of the steady Euler equations, an upwind finite volume technique has been applied. The solution method used is collective, symmetric point Gauss-Seidel relaxation, accelerated by non-linear multigrid. Initial finest grid solutions have been obtained by nested iteration. Automatic grid adaptation has been applied for obtaining sharp shocks. An indication is given of the mathematical quality of four different boundary conditions for the outlet flow. Two transonic flow solutions with shock are presented: a choked and a non-choked flow. Both flow solutions show good shock capturing. A comparison is made with experimental results.
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  • 32
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 113-120 
    ISSN: 0271-2091
    Keywords: Steady Navier-Stokes equations ; Partial flux splitting ; Multigrid 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: Flux splitting is applied to the convective part of the steady Navier-Stokes equations for incompressible flow. Partial upwind differences are introduced in the split first-order part, while central differences are used in the second-order part. The discrete set of equations obtained is positive, so that it can be solved by collective variants of relaxation methods. The partial upwinding is optimized in the same way as for a scalar convection-diffusion equation, but involving several Peclet numbers. It is shown that with the optimum partial upwinding accurate results can be obtained. A full multigrid method in W-cycle form, using red-black successive under-relaxation, injection and bilinear interpolation, is described. The efficiency of this method is demonstrated.
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  • 33
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 167-183 
    ISSN: 0271-2091
    Keywords: Axisymmetric turbulent flow ; Combustors ; Diffusers ; Navier-Stokes equations k-∊ model ; Zonal grid ; Finite differences ; 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: Numerical studies of turbulent flow in an axisymmetric 45° expansion combustor and bifurcated diffuser are presented. The Navier-Stokes equations incorporating a k-∊ model were solved in a non-orthogonal curvillinear co-ordinate system. A zonal grid method, wherein the flow field was divided into several subsections, was developed. This approach permitted different computational schemes to be used in the various zones. In addition, grid generation was made a more simple task. However, treatment of the zonal boundaries required special handling. Boundary overlap and interpolating techniques were used and an adjustment of the flow variables was required to assure conservation of mass flux. Three finite differencing methods - hybrid, quadratic upwind and skew upwind - were used to represent the convection terms. Results were compared with existing experimental data. In general, good agreement between predicted and measured values was obtained.
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  • 34
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 235-244 
    ISSN: 0271-2091
    Keywords: Process splitting ; Advection-dispersion equation ; Boundary conditions ; 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: Rational strategies are considered for the specification of the intermediate boundary condition at an inflow boundary where process splitting (fractional steps) is adopted in solving the advection-dispersion equation. Three lowest-order methods are initially considered and evaluation is based on comparisons with an analytical solution. For flow and dispersion parameter ranges typical of rivers and estuaries, the given boundary condition for the complete advection-dispersion equation at the end of the complete time step provides a satisfactory estimate of the intermediate boundary value. This was further confirmed by the development and evaluation of two higher-order methods. These required non-centred discrete approximations for spatial derivatives, which offset any special advantages from the higher truncation error order.
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  • 35
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 250-250 
    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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  • 36
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 263-273 
    ISSN: 0271-2091
    Keywords: Low-Reynolds-number flow ; Sedimentation ; Hydrodynamic interactions ; Two-phase flows ; Suspensions ; Boundary 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 new method for the simulation of the translational and rotational motions of a system containing a sedimenting particle interacting with a neutrally buoyant particle has been developed. The method is based on coupling the quasi-static Stokes equations for the fluid with the rigid body equations of motion for the particles. The Stokes equations are solved at each time step with the boundary element method. The stresses are then integrated over the surface of each particle to determine the resultant forces and moments. These forces and moments are inserted into the rigid body equations of motion to determine the translational and rotational motions of the particles. Unlike many other simulation techniques, no restrictions are placed on the shape of the particles. Superparametric boundary elements are employed to achieve accurate geometric representations of the particles. The simulation method is able to predict the local fluid velocity, resolve the forces and moments exerted on the particles, and track the particle trajectories and orientations.
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  • 37
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 369-373 
    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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    International Journal for Numerical Methods in Fluids 9 (1989), S. 363-368 
    ISSN: 0271-2091
    Keywords: Silencers ; Noise attenuation ; Shock flow ; Numerical simulation ; Gas dynamics ; 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 attenuating the noise from weapons firing is studied experimentally and numerically. As a possible method of attenuating the noise significantly, a silencer with no internal baffles is attached to the M242 cannon. The internal pressures inside the muffler are measured. The near-field overpressures outside the muffler at various polar angles are also measured. A numerical simulation of the flow through the muffler is performed, using Harten's shock-capturing method to solve the Euler equations of ideal compressible flow. The numerical simulation yields a detailed picture of the flow field as displayed by the pressure and Mach contours. Pressure-time curves at selected locations are obtained and compared with experimental data. There is good agreement, except that the numerical simulation generates more vigorous oscillations.
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  • 39
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 341-362 
    ISSN: 0271-2091
    Keywords: Unsteady ; Fluid flow ; Navier-Stokes ; Simulation ; SIMPLE ; PRIME ; QUICK ; ICCG ; MG ; 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 work builds on a SIMPLE-type code to produce two numerical codes of greatly improved speed and accuracy for solution of the Navier-Stokes equations. Both implicit and explicit codes employ an improved QUICK (quadratic upstream interpolation for convective kinematics) scheme to finite difference convective terms for non-uniform grids. The PRIME (update pressure implicit, momentum explicit) algorithm is used as the computational procedure for the implicit code. Use of both the ICCG (incomplete Cholesky decomposition, conjugate gradient) method and the MG (multigrid) technique to enhance solution execution speed is illustrated. While the implicit code is first-order in time, the explicit is second-order accurate. Two- and three-dimensional forced convection and sidewall-heated natural convection flows in a cavity are chosen as test cases. Predictions with the new schemes show substantial computational savings and very good agreement when compared to previous simulations and experimental data.
    Additional Material: 10 Ill.
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  • 40
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 374-374 
    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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  • 41
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1087-1098 
    ISSN: 0271-2091
    Keywords: RNS ; Separation ; Direct solver ; 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 reduced Navier-Stokes and thin layer approximations to the Navier-Stokes equations are used to obtain solutions for viscous subsonic three-dimensional flows. A spatial marching method is combined with a direct sparse matrix solver to obtain successive solutions in a global relaxation process. Results have been obtained for flow fields with and without regions of flow reversal.
    Additional Material: 12 Ill.
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  • 42
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1113-1119 
    ISSN: 0271-2091
    Keywords: Finite element ; Free streamlines ; Wakes ; 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 model having velocity components as basic unknowns is presented for calculation of two-dimensional flow past a symmetric profile with a wake in a channel. A modified least squares functional is used for the finite element solution of velocities. The determination of the position of the free streamline is treated as an optimum design problem. The concepts of cost function, geometry parameter and sensitivity derivative are employed. Numerical results are compared with published results obtained with streamfunction formulations.
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  • 43
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1165-1177 
    ISSN: 0271-2091
    Keywords: Laminar flow ; Triangular step ; FEM ; Velocity correction ; 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 velocity correction algorithm is used in the finite element method to solve forced convection problems between parallel plates with a triangular step, for Reynolds numbers up to 1000. Equal-order interpolation functions for velocity, pressure and temperature are used. The solutions show a smooth variation of pressure. The streamfunction, isotherms, isobars and velocity profiles are presented for a typical Reynolds number of 500. The skin friction and heat transfer results are presented for Reynolds numbers up to 1000.
    Additional Material: 6 Ill.
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  • 44
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1183-1193 
    ISSN: 0271-2091
    Keywords: CFD ; Transonics ; Streamfunction co-ordinates ; 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 has been developed for the computation of steady two-dimensional full-potential transonic flow past symmetric aerofoils. This method utilizes von Mises variables (x, ψ), where ψ is taken as the streamfunction for the flow. The flow equations and appropriate boundary conditions are formulated in terms of the von Mises variables (x, ψ) for symmetric aerofoils at zero incidence. This yields a system of two equations for unknowns ρ(x, ψ) and y(x, ψ). Finite difference solutions have been computed using SLOR at subcritical and supercritical Mach numbers. The results are compared with available data and are in excellent agreement.
    Additional Material: 5 Ill.
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  • 45
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1221-1234 
    ISSN: 0271-2091
    Keywords: Biharmonic equation ; Stokes flow ; Simple layer potential ; Method of fundamental 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: A novel formulation of the method of fundamental solutions for the numerical solution of plane biharmonic problems, based on the simple layer potential representation of Fichera, is presented. The applicability and accuracy of the method are demonstrated by examining its performance on a set of practical problems arising in Stokes fluid flow.
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  • 46
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1285-1298 
    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; Vorticity-velocity ; Multiconnected domains ; Pressure single-valuedness ; 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 thermofluid dynamic fields in two-dimensional multiconnected domains are analysed by solving the Navier-Stokes equations with the Boussinesq approximation in the vorticity-velocity formulation. The need of an integral condition for the pressure to be single-valued on each independent irreducible loop, in analogy with the ω-Ψ formulation, is demonstrated. The field equations are discretized by a finite difference technique and solved at the steady state via an alternating direction implicit method of a scalar type. Two test cases at low Reynolds and Rayleigh numbers are considered: the multiconnected driven cavity and an annulus with isothermal walls and stationary or rotating inner cylinder.
    Additional Material: 12 Ill.
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  • 47
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1302-1304 
    ISSN: 0271-2091
    Keywords: Incompressible flow ; Clebsch potentials ; 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: A recent paper by W. Zijl, which reformulated the Navier-Stokes and Boussinesq equations in terms of Clebsch potentials, has an error that greatly reduces the generality of the results. Some other recent efforts to use such potentials in fluid and plasma dynamics are briefly discussed.
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  • 48
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 569-582 
    ISSN: 0271-2091
    Keywords: Flow analysis ; Free surface problem ; Finite element method ; Blast furnace ; 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 sharp interface problem arising in the flow of two immiscible fluids, slag and molten metal in a blast furnace, is formulated using a two-dimensional model and solved numerically. This problem is a transient two-phase free or moving boundary problem, the slag surface and the slag-metal interface being the free boundaries. At each time step the hydraulic potential of each fluid satisfies the Laplace equation which is solved by the finite element method. The ordinary differential equations determining the motion of the free boundaries are treated using an implicit time-stepping scheme. The systems of linear equations obtained by discretization of the Laplace equations and the equations of motion of the free boundaries are incorporated into a large system of linear equations. At each time step the hydraulic potential in the interior domain and its derivatives on the free boundaries are obtained simultaneously by solving this linear system of equations. In addition, this solution directly gives the shape of the free boundaries at the next time step. The implicit scheme mentioned above enables us to get the solution without handling normal derivatives, which results in a good numerical solution of the present problem. A numerical example that simulates the flow in a blast furnace is given.
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  • 49
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 943-962 
    ISSN: 0271-2091
    Keywords: Navier-Stokes solver ; Vortex motion ; Finite volume method ; Viscous flow ; Delta wing ; 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 3D Navier-Stokes solver has been developed to simulate laminar compressible flow over quadrilateral wings. The finite volume technique is employed for spatial discretization with a novel variant for the viscous fluxes. An explicit three-stage Runge-Kutta scheme is used for time integration, taking local time steps according to the linear stability condition derived for application to the Navier-Stokes equations. The code is applied to compute primary and secondary separation vortices at transonic speeds over a 65° swept delta wing with round leading edges and cropped tips. The results are compared with experimental data and Euler solutions, and Reynolds number effects are investigated.
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  • 50
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1059-1072 
    ISSN: 0271-2091
    Keywords: Viscoelastic flow ; Leonov model ; Convective integration ; 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 finite element method is used to find the elastic strain (and thus the stress) for given velocity fields of the Leonov model fluid. With a simple linearization technique and the Galerkin formulation, the quasi-linear coupled first-order hyperbolic differential equations together with a non-linear equality constraint are solved over the entire domain based on a weighted residual scheme. The proposed numerical scheme has yielded efficient and accurate convective integrations for both the planar channel and the diverging radial flows for the Leonov model fluid. Only the strain in the inflow plane is required to be prescribed as the boundary conditions. In application, it can be conveniently incorporated in an existing finite element algorithm to simulate the Leonov viscoelastic fluid flow with more complex geometry in which the velocity field is not known a priori and an iterative procedure is needed.
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  • 51
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1321-1329 
    ISSN: 0271-2091
    Keywords: Peaceman-Rachford ADI method ; Method of sweeps ; Central differences of o(h2; k2) ; Rotating viscous fluid ; 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 flow of steady incompressible viscous fluid rotating about the z-axis with angular velocity ω and moving with velocity u past a sphere of radius a which is kept fixed at the origin is investigated by means of a numerical method for small values of the Reynolds number Reω. The Navier-Stokes equations governing the axisymmetric flow can be written as three coupled non-linear partial differential equations for the streamfunction, vorticity and rotational velocity component. Central differences are applied to the partial differential equations for solution by the Peaceman-Rachford ADI method, and the resulting algebraic equations are solved by the ‘method of sweeps’.The results obtained by solving the non-linear partial differential equations are compared with the results obtained by linearizing the equations for very small values of Reω. Streamlines are plotted for Ψ = 0·05, 0·2, 0·5 for both linear and non-linear cases. The magnitude of the vorticity vector near the body, i.e. at z = 0·2, is plotted for Reω = 0·05, 0·24, 0·5. The correction to the Stokes drag as a result of rotation of the fluid is calculated.
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  • 52
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1413-1426 
    ISSN: 0271-2091
    Keywords: Impinging jet ; MacCormack implicit scheme ; Implicit bidiagonal numerical 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: Two-dimensional normal impinging jet flowfields, with or without an upper plate, were analysed by employing an implicit bidiagonal numerical method developed by Lavante and Thompkins Jr. The Jones-Launder K-∊ two-equation turbulent model was employed to study the turbulent effects of the impinging jet flowfield. The upper plate surface pressure, the ground plane pressure and other physical parameters of the momentum flowfield were calculated at various jet exit height and jet inlet Reynolds numbers. These results were compared with those of Beam and Warming's numerical method, Hsiao and Chuang, and others, along with experimental data. The potential core length of the impinging jet without an upper plate is longer than that of the free jet because of the effects of the ground plane, while the potential core length of the impinging jet with an upper plate is shorter than that of the free jet because of the effects of the upper plate. This phenomenon in the present analysis provides a fundamental numerical study of an impinging jet and a basis for further analysis of impinging jet flowfields on a variable angle plate.
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  • 53
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    International Journal for Numerical Methods in Fluids 9 (1989) 
    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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    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1431-1451 
    ISSN: 0271-2091
    Keywords: Probabilistic diffusion-convection equation ; Gaussian field approach ; Random walk method ; Fluctuation Peclet number ; Porous media ; Two-phase system ; 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 channels formed between individual particles in porous media have variable dimensions and orientations. The porosity, permeability and its anisotropy exhibit random spatial distributions. The probabilistic approach can effectively describe the transport of contaminants through porous media and is analysed in this paper. Numerical results are obtained by considering (I) random dispersion coefficients without and with spatial structure, (II) random time distribution of concentration at the inlet boundary, (III) random velocity distribution in the flow field without and (IV) with variable dispersion coefficient, (V) non-linearity of the governing equation and (VI) anisotropy of the dispersion coefficient. Two methods are used for probabilistic predictions: (1) Gaussian field approach in conjunction with Monte Carlo method and (2) random walk method. The input random parameters are assumed to have normal and log-normal distributions according to available experimental data. The probability distribution functions of the contaminant concentration at different locations within the flow domain are calculated and compared with the input distributions as a function of the mean and fluctuation Peclet numbers. The one-dimensional case is analysed in detail and the illustrative numerical predictions are compared with analytical and experimental results. The extension to a two-dimensional domain is discussed in the last part of this paper.
    Additional Material: 16 Ill.
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  • 55
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    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1539-1542 
    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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  • 56
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    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 13 (1989), S. 459-476 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A closed-form analysis for elastic - plastic response of a circular hole in an infinite Mohr - Coulomb medium under axisymmetric loading shows the effect of repeated loading on the stress and displacement fields around the hole. Examples show how repeat-load closure increment is affected by working load, internal pressure, material compressive strength and internal friction. The solution is used to predict results of a laboratory test performed on a rock simulant specimen that contained a reinforced hole. Analytical and laboratory results are similar: at small closures (a few per cent, but well into the plastic response range), the closure increment from an unload - reload cycle is small compared with the initial closure. Closure increments for each of several cycles are comparable and cumulative.
    Additional Material: 7 Ill.
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  • 57
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    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 13 (1989), S. 531-550 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A new semi-analytical solution for the transport of a conservative contaminant species in a fractured medium having a regular two- or three-dimensional fracture network is presented. The application of the technique and some of the practical implications arising from an examination of contaminant migration in fractured systems is discussed. Particular consideration is given to the effects of Darcy velocity, fracture spacing, matrix porosity, dispersivity and the mass of contaminant available for transport. The implications of uncertainty with respect to fracture opening size and ground-water velocity is also discussed and it is shown that provided one can obtain a reasonable estimate of the hydraulic gradient and hydraulic conductivity for the rock mass, uncertainty regarding the magnitude of the opening size and the groundwater velocity does not have a significant effect on predicted contaminant migration for the class of problems being considered.
    Additional Material: 13 Ill.
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  • 58
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    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 13 (1989), S. 551-564 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A numerical technique has been implemented to perform strain path analyses for arbitrary three-dimensional (3D) penetrometers. The technique is based on that developed in aeronautical engineering for the calculation of incompressible potential flows about arbitrary 3D, non-lifting bodies. It uses a source-density distribution on the surface of the body and solves for the distribution necessary to make the normal component of fluid velocity zero on the boundary. The surface of a 3D body is approximated by a series of plane quadrilaterals, and the integral equation for the source density is replaced by a set of linear algebraic equations which are then solved for the source densities on the quadrilaterals. The displacements and strains are eventually derived based on these source densities. A series of strain-path analyses have been performed for cone and flat dilatometer penetrations. Results show that the soil responses to these two types of penetrometers are fundamentally different.
    Additional Material: 9 Ill.
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  • 59
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    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 13 (1989), S. 575-598 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: There are many expressions proposed for the permeability of isotropic media based on flow channel and pore size distribution concepts, but there are no such expressions for anisotropic media. In this paper an expression for the permeability of an anisotropic medium is proposed, which has been verified in the laboratory.The mechanism behind fluid flow through soil was investigated using microscopic computer simulations to propose an expression for macroscopic permeability. The soil was assumed to be a spatially periodic porous medium, and the Navier-Stokes equation was solved using the FEM with appropriate boundary conditions for several different arrangements of the porous medium. The basic variables influencing flow through soil at the microscopic level were identified as specific surface area, void ratio, particle shape, material heterogeneity and the arrangement of particles in a porous medium. A sensitivity analysis was carried out to obtain an expression for the permeability in terms of the above variables.The corresponding macroscopic variables for the above microscopic variables are average specific surface area, average void ratio, anisotropy, tortuosity due to material heterogeneity, and the arrangement of particles respectively. An expression for the directional permeability is proposed in terms of these variables for the most common occurrence of particles in a porous medium.For the verification of the proposed equation, the permeability values of a fine-grained sand were measured at different void ratios and were compared with those predicted by the proposed equation. The results show that the predicted permeability values from the proposed equation are very close to the measured values.
    Additional Material: 14 Ill.
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  • 60
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    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 13 (1989), S. 675-675 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Type of Medium: Electronic Resource
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  • 61
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    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 13 (1989), S. 629-644 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: The stiffness characteristics of a packing of granules are influenced by the particle interactions at contacts, the void ratio, the co-ordination number and the packing structure. A stress-strain relationship for the packings of spheres is presented. The relationship explicitly includes the contact force-displacement law and the parameters characterizing the packing structure. The initial moduli computed using this relationship are compared with experimental measurements and empirical equations for sands. The theoretical results are also compared with experimental results on packings of glass balls. Closed-form solutions are derived for statistically isotropic packings under initial isotropic stress conditions. Numerical solutions for the stiffness properties are obtained for anisotropic initial stress conditions and anisotropic packing structures.
    Additional Material: 11 Ill.
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  • 62
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    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 13 (1989), S. 677-680 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Type of Medium: Electronic Resource
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