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Canonical-variables multigrid method for Euler equations

  • S. Ta'asan
3. Numerical Methods and Algorithms b) Grids/Acceleration Techniques
Part of the Lecture Notes in Physics book series (LNP, volume 453)

Abstract

In this paper we describe a novel approach for the solution of inviscid flow problems for subsonic compressible flows. The approach is based on canonical forms of the equations, in which subsystems governed by hyperbolic operators are separated from those governed by elliptic ones. The discretizations used as well as the iterative techniques for the different subsystems, are inherently different. Hyperbolic parts, which describe, in general, propagation phenomena, are discretized using upwind schemes and are solved by marching techniques. Elliptic parts, which are directionally unbiased, are discretized using h-elliptic central discretizations, and are solved by pointwise relaxations together with coarse grid acceleration. The resulting discretization schemes introduce artificial viscosity only for the hyperbolic parts of the system; thus a smaller total artificial viscosity is used, while the multigrid solvers used are much more efficient. Solutions of the subsonic compressible Euler equations are achieved at the same efficiency as the full potential equation.

Keywords

Euler Equation Canonical Form Coarse Grid Streamwise Direction Multigrid Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    A. Brandt: Multigrid Techniques 1984 Guide with Applications to Fluid Dynamics. GMD Studien Nr 85.Google Scholar
  2. [2]
    A. Brandt and S. Ta'asan: Multigrid Solutions to Quasi-Elliptic Schemes. In Progress and Supercomputing in Computational Fulid Dynamics Proceedings of the U.S.-Israel Workshop 1984, Earll. M. Murman and Saul Abarbanel (Eds.), Birkhauser 1985Google Scholar
  3. [3]
    Hemker, P.W.: Defect Correction and Higher Order Schemes for the Multigrid Solution of the Steady Euler Equations, Multrigrid Methods II, W. Hackbush and U. Trottenberg (Eds), (Lecture Motes in Mathematics Springer Verlag, Berlin, 149–165.Google Scholar
  4. [4]
    A. Jameson: Solution of the Euler Equations for Two Dimensional Transonic Flow by Multigrid Method, appl. Math. and Computat., 13, 327–355.Google Scholar
  5. [5]
    S. Ta'asan: Canonical forms of Multidimensionl Inviscid Flows. ICASE Report No. 93-34Google Scholar
  6. [6]
    S. Ta'asan: Canonical-Variables Multigrid Method for Steady-State Euler Equations. ICASE Report No. 94-14Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • S. Ta'asan
    • 1
  1. 1.NASA Langley Research CenterInstitute for Computer Applications in Science and EngineeringHampton, VAUSA

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