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  • 11
    Electronic Resource
    Electronic Resource
    A poisson equation formulation for pressure calculations in penalty finite element models for viscous incompressible flows (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 349-361 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The calculation of pressures when the penalty function approximation is used in finite element solutions of laminar incompressible flows is addressed. A Poisson equation for the pressure is formulated that involves third derivatives of the velocity field. The second derivatives appearing in the weak formulation of the Poisson equation are calculated from the C0 velocity approximation using a least squares method. The present scheme is shown to be efficient, free of spurious oscillations, and accurate. Examples of applications are given and compared with results obtained using mixed formulations.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620300209
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    Paper (German National Licenses)
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  • 12
    Electronic Resource
    Electronic Resource
    Physically correct penalty-like formulations for accurate pressure calculation in finite element algorithms of the Navier-Stokes equations (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 3883-3902 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element algorithms for incompressible fluids, in particular the penalty function method, are re-examined and re-formulated based on physically consistent approximations to the mass conservation equation. These approximations lead to methods that satisfy all fluid conditions under the assumption of slightly compressible flow and directly yield approximations to the pressure field that are free from spurious oscillations. Penalty function-type algorithms are developed for direct steady-state calculations and for time-dependent simulations of viscous incompressible flows that are based on the bilinear isoparametric quadrilateral element and circumvent the Ladyszhenskaya, Babuska and Brezzi (LBB) condition. Further-more, methods that eliminate pressure oscillations in the low Mach number region of high-speed compressible flows are obtained. These methods are tested in examples that show their superior performance in approximating the pressure field.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620362208
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    Paper (German National Licenses)
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  • 13
    Electronic Resource
    Electronic Resource
    On boundary conditions for unbounded flows (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 179-185 
    Details
    ISSN: 1069-8299
    Keywords: finite elements ; fluid flow ; open boundaries ; Sommerfield boundary conditions ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We examine a method to impose boundary conditions on arbitrary boundaries, introduced to make domains of infinite extent finite for the purpose of numerical calculations, when a finite element discretization based on linear, bilinear or trilinear elements is used, in one, two or three dimensions, respectively. In particular, we look at the so-called ‘free’ boundary condition, which consists in retaining the boundary integrals generated by the weighted-residuals formulation along the open boundaries and adding them to the stiffness matrix. We show that this procedure is exactly equivalent to imposing on the boundary nodes a Sommerfeld radiation condition in one dimension, and a slightly modified form of the Sommerfeld boundary condition in two and three dimensions. We also show that the procedure is not applicable to the purely elliptic case.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110211
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  • 14
    Electronic Resource
    Electronic Resource
    Quadratic finite element schemes for two-dimensional convective-transport problems (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1831-1844 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620111207
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  • 15
    Electronic Resource
    Electronic Resource
    Solution of the Pontriagin-Vitt equation for the moments of time to first passage of the randomly accelerated particle by the finite element method (1980)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 1408-1412 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Pontriagin-Vitt equation governing the mean of the time of first passage of a randomly accelerated particles has been studied extensively by Franklin and Rodemich.1 In their paper is presented the analytic solution for the two-sided barrier problem and solutions by several finite difference procedures.This note demonstrates solution of the problem by a Petrov-Galerkin finite element method using upstream weighting functions,2 shown to give rapidly convergent results. In addition, the equation is generalized to include higher statistical moments, and solutions for the first few ordinary moments are reported.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620150913
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  • 16
    Electronic Resource
    Electronic Resource
    On quadratic elements in finite element solutions of steady-state convection - diffusion equation (1980)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 1041-1052 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620150706
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    Paper (German National Licenses)
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  • 17
    Electronic Resource
    Electronic Resource
    On the reliability of the linear oscillator and systems of coupled oscillatorsDedicated to Professor O. C. Zienkiewicz on the occasion of his sixtieth birthday. (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1271-1295 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 20 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620180902
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    Paper (German National Licenses)
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  • 18
    Electronic Resource
    Electronic Resource
    BOUNDARY CONDITIONS FOR FINITE ELEMENT SIMULATIONS OF CONVECTIVE FLOWS WITH ARTIFICIAL BOUNDARIES (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 1053-1071 
    Details
    ISSN: 0029-5981
    Keywords: finites elements ; open boundaries ; fluid flow ; natural boundary conditions ; Sommerfeld raiation condition ; Navier-Stokes equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We examine the use of natural boundary conditions and conditions of the Sommerfeld type for finite element simulations of convective transport in viscous incompressible flows. We show that natural boundary conditions are superior in the sense that they always provide a correct boundary condition, as opposed to the Sommerfeld-type conditions, which can lead to a singular formulation and a great loss of accuracy. For the Navier-Stokes equations, the natural boundary conditions must be combined with a simple method to eliminate perturbations on the pressure at the open boundary, which is the source of most errors.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
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