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Flux-vector splitting for the Euler equations

  • Bram van Leer
Contributed Papers
Part of the Lecture Notes in Physics book series (LNP, volume 170)

Abstract

For the full or isenthalpic Euler equations combined with the ideal-gas law, the flux-vector splitting presented here is, by a great margin, the simplest means to implement upwind differencing. For a polytropic gas law, with γ > 1, closed formulas have not yet been derived.

The scheme produces steady shock profiles with two interior zones. There is evidence [10] that, among implicit versions of upwind methods, those with a two-zone steady-shock representation give faster convergence to a steady solution than those with a one-zone representation.

A disadvantage in using any flux-vector splitting is that it leads to numerical diffusion of a contact discontinuity at rest. This diffusion can be removed; present research is aimed at achieving this with minimal computational effort.

Numerical solutions by first- and second-order schemes including the above split fluxes can be found in Refs. [6], [7] (one-dimensional) and [8], r91 (two-dimensional).

Keywords

Mach Number Euler Equation Contact Discontinuity Shock Structure Steady Solution 
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.
    P.L. Roe, J. Computational Phys. 43 (1981), 357.CrossRefGoogle Scholar
  2. 2.
    S. Osher, “Numerical solution of singular perturbation problems and hyperbolic systems of conservation laws”, North-Holland Mathematical Studies 47 (1981), 179.TGoogle Scholar
  3. 3.
    R.H. Sanders and K.H. Prendergast, Astrophys. J. 188 (1974), 489.Google Scholar
  4. 4.
    J.L. Steger and R.F. Warming, J. Computational Phys. 40 (1981), 263.Google Scholar
  5. 5.
    A. Harten, P.D. Lax and B. van Leer, “Upstream differencing and Godunov-type schemes”, ICASE Report No. 82-5; to appear in SIAM Review.Google Scholar
  6. 6.
    J.L. Steger, “A preliminary study of relaxation methods for the inviscid conservative gasdynamics equations using flux-vector splitting”, Report No. 80-4, August 1980, Flow Simulations, Inc.Google Scholar
  7. 7.
    G.D. van Albada, B. van Leer and W.W. Roberts, Jr., “A comparative study of computational methods in cosmic gas dynamics”, Astron. Astrophys. 108 (1982), 76.Google Scholar
  8. 8.
    G.D. van Albada and W.W. Roberts, Jr., Ap. J. 246 (1981), 740.Google Scholar
  9. 9.
    M.D. Salas, “Recent developments in transonic flow over a circular cylinder”, NASA Technical Memorandum 83282 (April 1982).Google Scholar
  10. 10.
    P.M. Goorjian and R. van Buskirk, “Implicit calculations of transonic flow using monotone methods”, AIAA Paper 81-331 (198,1).Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Bram van Leer
    • 1
  1. 1.Leiden University ObservatoryRA, LeidenThe Netherlands

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