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About splitting and non-splitting schemes for conservation laws in 2-D

  • Dietmar Kröner
Conference paper
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NNFM, volume 29)

Abstract

In this paper we shall discuss some problems which may arise in the context of dimensional splitting for conservation laws. We shall study a directionally adapted scheme which has better stability properties at least for anisotropic scalar equations in 2-D. This algorithm can be generalized to the non-linear unsteady Euler equations in 2-D and can be used to reduce the system locally to a scalar equation in 2-D.

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References

  1. [COL]
    P. Colella, Multidimensional upwind methods for hyperbolic conservation laws. Report Lawrence Berkeley Laboratory 17023, 1984.Google Scholar
  2. [COO]
    C.H. Cooke, On operator splitting of the Euler equations consistent with Har-ten’s second-order accurate TVD scheme. Numerical methods for partial differential equations. 1(1985), 315–327.MathSciNetzbMATHCrossRefGoogle Scholar
  3. [DAV]
    S.F. Davis, A rotationally biased upwind difference scheme for the Euler equations. J. of Comp. Physics 56(1984), 65–92.ADSzbMATHCrossRefGoogle Scholar
  4. [HLD]
    Ch. Hirsch, C. Lacor, H. Deconinck, Convection algorithm on a diagonal procedure for the multidimensional Euler equation. AIAA, Proceedings of the 8-th Computational Fluid Dynamics Conference 1987.Google Scholar
  5. [KR1]
    D. Kröner/Numerical schemes for the Euler equations in two space dimensions without dimensional splitting. Proceedings of the 2-nd International Conference on Nonlinear Hyperbolic Equations-Theory, Computation Methods, and Applications. Notes on Numerical Fluid Mechanics, Vol. 24, Braunschweig 1989.Google Scholar
  6. [KR2]
    D. Kröner. Directionally adapted upwind schemes in 2-D for the Euler equations. DFG Priority Research Programme, Results 1986–1988, Notes on Numerical Fluid Mechanics, Vol. 25, Braunschweig 1989.Google Scholar
  7. [LV1]
    R.J. LeVeque, High resolution finite volume methods on grids via wave propagation. ICASE report 87-68, 1987Google Scholar
  8. [LV2]
    R.J. LeVeque, Cartesian grid methods for flow in irregular regions. To appear in the Proceedings of the Oxford Conference on Numerical Methods in Fluid Dynamics, 1988.Google Scholar
  9. [RM]
    R.D. Richtmyer, K.W. Morton, Difference methods for initial-value problems. Second edition, New York 1967.Google Scholar
  10. [RO1]
    P. Roe, A basis for upwind differentiating of the two dimensional unsteady Euler equations. Numerical methods for fluid dynamics II, Eds.: Morton, Baines, Oxford Univ. Press 1986.Google Scholar
  11. [RO2]
    P. Roe, Linear advection schemes on triangular meshes. CoA Report No 8720, Cranfield 1987.Google Scholar
  12. [RO3]
    P. Roe, Discontinuous solutions to hyperbolic systems under operator splitting. Manuscript.Google Scholar
  13. [SMO]
    J. Smoller, Shockwaves and reaction-diffusion equations. New York Heidelberg Berlin 1983.Google Scholar
  14. [SOD]
    G.A. Sod, Numerical methods in fluid dynamics. Initial and initial boundary value problems. Cambridge 1985.Google Scholar

Copyright information

© Springer Fachmedien Wiesbaden 1990

Authors and Affiliations

  • Dietmar Kröner
    • 1
  1. 1.Fachbereich MathematikUniversität des SaarlandesSaarbrückenGermany

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