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  • 1
    Electronic Resource
    Electronic Resource
    ARTIFICIAL BOUNDARIES AND FLUX AND PRESSURE CONDITIONS FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 325-352 
    Details
    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; artificial boundary conditions ; flux and pressure conditions ; finite elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Fluid dynamical problems are often conceptualized in unbounded domains. However, most methods of numerical simulation then require a truncation of the conceptual domain to a bounded one, thereby introducing artificial boundaries. Here we analyse our experience in choosing artificial boundary conditions implicitly through the choice of variational formulations. We deal particularly with a class of problems that involve the prescription of pressure drops and/or net flux conditions.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 2
    Electronic Resource
    Electronic Resource
    A COMPARATIVE STUDY OF TIME-STEPPING TECHNIQUES FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS: FROM FULLY IMPLICIT NON-LINEAR SCHEMES TO SEMI-IMPLICIT PROJECTION METHODS (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 987-1011 
    Details
    ISSN: 0271-2091
    Keywords: non-stationary incompressible Navier-Stokes equations ; time-stepping schemes ; projection 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: We present a numerical comparison of some time-stepping schemes for the discretization and solution of the non-stationary incompressible Navier- Stokes equations. The spatial discretization is by non-conforming quadrilateral finite elements which satisfy the LBB condition. The major focus is on the differences in accuracy and efficiency between the backward Euler, Crank-Nicolson and fractional-step Θ schemes used in discretizing the momentum equations. Further, the differences between fully coupled solvers and operator-splitting techniques (projection methods) and the influence of the treatment of the nonlinear advection term are considered. The combination of both discrete projection schemesand non-conforming finite elementsallows the comparison of schemes which are representative for many methods used in practice. On Cartesian grids this approach encompasses some well-known staggered grid finite difference discretizations too. The results which are obtained for several typical flow problems are thought to be representative and should be helpful for a fair rating of solution schemes, particularly in long-time simulations.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Tools for simulating non-stationary incompressible flow via discretely divergence-free finite element models (1994)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 71-105 
    Details
    ISSN: 0271-2091
    Keywords: Non-stationary ; Navier-Stokes equations ; Upwind ; Divergence-free finite elements ; Multigrid ; Visualization ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We develop simulation tools for the non-stationary incompressible 2D Navier--Stokes equations. The most important components of the finite element code are: the fractional step ϑ-scheme, which is of second-order accuracy and strongly A-stable, for the time discretization; a fixed point defect correction method with adaptive step length control for the non-linear problems (stationary Navier-Stokes equations); a modified upwind discretization of higher-order accuracy for the convective terms. Finally, the resulting nonsymmetric linear subproblems are treated by a special multigrid algorithm which is adapted to the quadrilateral non-conforming discretely divergence-free finite elements. For the graphical postprocess we use a fully non-stationary and interactive particle-tracing method. With extensive test calculations we show that our method is a candidate for a ‘black box’ solver.
    Additional Material: 33 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650180105
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