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  • finite element method  (6)
  • Linear Interpolation  (2)
  • Selective Lumping Method  (2)
  • Bilinear interpolation functions  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Optimal control of vorticity in Rayleigh-Bernard convection by finite element method (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 9-22 
    Details
    ISSN: 1069-8299
    Keywords: finite element method ; optimal control theory ; Navier-Stokes equations ; Lagrange multipliers ; adjacent equations ; Sakawa-Shindo method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This work presents control of vorticity for buoyancy-driven flows. The governing set of equations includes Navier-Stokes and heat transfer equations. The basic formulation for the control problem is derived using Lagrange multipliers and the Pontryagin minimum principle. Control values are found using the Sakawa-Shindo method. Control was accomplished using velocity components. Numerical examples present control of vorticity for Rayleigh-Bernard convection in an enclosed cavity for a wide range of Ra numbers. The current formulation proved reliable and fast. Optimal control was obtained and turned out to be adequate. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 2
    Electronic Resource
    Electronic Resource
    Finite element analysis of density flow using the velocity correction method (1985)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 981-993 
    Details
    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.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650051104
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  • 3
    Electronic Resource
    Electronic Resource
    MODEL VERIFICATION ON 3D TIDAL CURRENT ANALYSIS IN TOKYO BAY (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 43-66 
    Details
    ISSN: 0271-2091
    Keywords: multiple-level model ; finite element method ; open boundary condition ; tidal current 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 results of a research project to verify the newly improved multiple- level model for 3D tidal current analysis in Tokyo Bay are presented. The improved multiple-level model includes additional effects due to Coriolis force, river inflows and wind shear stresses. Furthermore, a new numerical treatment of the open boundary condition was applied which effectively eliminated the spurious reflective waves often generated by various numerical methods simulating free surface flows. The mean (time-averaged or residual) and tidal currents in Tokyo Bay were simulated as examples to demonstrate the validity and capability of the newly improved multiple-level model. A series of numerical experiments was conducted to carefully examine the tidal circulations affected by the forcing factors of Coriolis force, river inflows and wind shears, both individually and combined. The numerical results demonstrated that the effects of each forcing term are physically reasonable, with the wind shear effect being the most significant and the case including all forcing terms being in best overall agreement with the field data collected in Tokyo Bay by the Ministry of Transportation. This study has contributed not only to the verification of the newly improved multiple-level model but also to the enhancement of the accuracy of numerical simulations of three-dimensional flow in coastal waters by this model.
    Additional Material: 22 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    COMPARISON OF SENSITIVITY EQUATION AND ADJOINT EQUATION METHODS FOR PARAMETER IDENTIFICATION PROBLEMS (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 1015-1024 
    Details
    ISSN: 0029-5981
    Keywords: parameter identification ; thermal conduction ; sensitivity equation ; adjoint equation ; finite element method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper deals with the inverse analysis of a thermal conduction problem, in which the thermal conductivity is identified as an unknown parameter, which is determined so as to minimize the cost function represented by the square of the difference between the computed and observed temperatures at pre-assigned observation points. To minimize the cost function, both sensitivity equation and adjoint equation methods can be adopted. The sensitivity equation can be introduced by differentiating the governing equation directly. The sensitivity coefficient is obtained by the sensitivity equation. The adjoint equation is introduced via a variational approach using a Lagrange multiplier. The Lagrange multiplier is solution to an adjoint equation. Both sensitivity coefficient and Lagrange multiplier are used to calculate the gradient of the cost function. The purpose of this paper is to compare the sensitivity equation and adjoint equation methods from the convergence and computational efficiency points of view. © 1997 by John Wiley & Sons, Ltd.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Arbitrary Lagrangian-Eulerianc finite element method for unsteady, convective, incompressible viscous free surface fluid flow (1987)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 7 (1987), S. 1053-1075 
    Details
    ISSN: 0271-2091
    Keywords: ALE Method ; Incompressible Viscous Flow ; Velocity Correction Method ; Free Surface ; 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: In this paper, free surface flow problems involving large free surface motions are analysed using finite element techniques. In solving these problems an arbitrary Lagrangian-Eulerian (ALE) kinematical description of the fluid domain is adopted, in which the nodal points can be displaced independently of the fluid motion. This formulation leads to an easy and accurate treatment of fluid-fluid interfaces, and greater distortions in the fluid motions can be handled than would be allowed by a purely Lagrangian method.This paper describes the basic methodology, presents finite element approximations and discusses such matters as stability, accuracy and rezoning. The generality and the advantage of the present method are discussed, and its versatility is demonstrated through a few numerical experiments.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650071005
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  • 6
    Electronic Resource
    Electronic Resource
    Parameter identification and optimal control of ground temperature (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 20 (1995), S. 789-801 
    Details
    ISSN: 0271-2091
    Keywords: identification ; optimal control ; finite element method ; temperature control 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: To avoid the use of pesticides on putting greens of golf courses, a temperature regulator system is strongly recommended nowadays in Japan. To maintain grass on the putting green without pesticide, the temperature of the ground should be controlled. This system consists of a cooling machine and buried pipes in the ground. The temperature of the water in the pipes cannot be regulated. In this paper, both identification and control problems are presented by the minimization technique and applied to a practical problem. To establish the system, it is important to obtain accurate parameters which are included in the governing equation. These parameters can be determined by parameter identification. The conjugate gradient method is used for the parameter identification procedure. The control problem aims to make the temperature at arbitrary points close to the objective temperature. The discrete-time dynamic programming is used for the control procedure.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650200807
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  • 7
    Electronic Resource
    Electronic Resource
    Selective lumping finite element method for shallow water flow (1982)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982), S. 89-112 
    Details
    ISSN: 0271-2091
    Keywords: Two Step Scheme ; Selective Lumping Method ; Tidal Flow ; Osaka Bay ; 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 for solving shallow water flow problems is presented. The standard Galerkin method is employed for spatial discretization. The numerical integration scheme for the time variation is the explicit two step scheme, which was originated by the authors and their co-workers. However, the original scheme has been improved to remove the erroneous artifical damping effect. Since the improved scheme employs a combination of lumped and unlumped coefficients, the scheme is referred to as a selective lumping scheme. Stability conditions and accuracy are investigated by considering several numerical examples. The method has been applied to the tidal flow in Osaka Bay and Yatsushiro Bay.
    Additional Material: 18 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650020106
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  • 8
    Electronic Resource
    Electronic Resource
    Two-step explicit finite element method for two-layer flow analysis (1984)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 4 (1984), S. 931-947 
    Details
    ISSN: 0271-2091
    Keywords: Two-layer Flow ; Two-step Scheme ; Selective Lumping Method ; Ishikari Bay ; 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 for the analysis of two-layer density flows is presented in this paper. The standard Galerkin method based on linear interpolation functions is used to yield discrete spatial variables. For numerical integration in time, an explicit two-step selective lumping method is used. Here it is applied to a flow analysis of Ishikari Bay, at the mouth of Ishikari River. This case demonstrates a procedure that yields a numerically stable solution.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650041004
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  • 9
    Electronic Resource
    Electronic Resource
    A finite element scheme based on the velocity correction method for the solution of the time-dependent incompressible Navier-Stokes equations (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 403-423 
    Details
    ISSN: 0271-2091
    Keywords: Velocity correction method ; Bilinear interpolation functions ; Pressure 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: In this paper a finite element solution for two-dimensional incompressible viscous flow is considered. The velocity correction method (explicit forward Euler) is applied for time integration. Discretization in space is carried out by the Galerkin weighted residual method. The solution is in terms of primitive variables, which are approximated by piecewise bilinear basis functions defined on isoparametric rectangular elements. The second step of the obtained algorithm is the solution of the Poisson equation derived for pressure. Emphasis is placed on the prescription of the proper boundary conditions for pressure in order to achieve the correct solution. The scheme is completed by the introduction of the balancing tensor viscosity; this makes this method stable (for the advection-dominated case) and permits us to employ a larger time increment. Two types of example are presented in order to demonstrate the performance of the developed scheme. In the first case all normal velocity components on the boundary are specified (e.g. lid-driven cavity flow). In the second type of example the normal derivative of velocity is applied over a portion of the boundary (e.g. flow through sudden expansion). The application of the described method to non-isothermal flows (forced convection) is also included.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130402
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  • 10
    Electronic Resource
    Electronic Resource
    Linear stability of incompressible fluid flow in a cavity using finite element method (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 27 (1998), S. 139-157 
    Details
    ISSN: 0271-2091
    Keywords: hydrodynamic stability ; finite element method ; incompressible cavity flow ; Arnold's method ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Numerical methods have been applied to theoretical studies of instability and transition to turbulence. In this study an analysis of the linear stability of incompressible flow is undertaken. By means of the finite element method the two-dimensional base flow is computed numerically over a range of Reynolds numbers and is perturbed with three-dimensional disturbances. The partial differential equations governing the evolution of perturbation are obtained from the non-linear Navier-Stokes equations with a slight compressibility by using linear stability and normal mode analysis. In terms of the finite element discretization a non-singular generalized eigenproblem is formulated from these equations whose solution gives the dispersion relation between complex growth rate and wave number. This study presents stability curves to identify the critical Reynolds number and critical wavelength of the neutral mode and discusses the mechanism of instability. The stability of lid-driven cavity flow is examined. Taylor-Göertler-like vortices in the cavity are obtained by means of reconstruction of three-dimensional flows. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
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