Flux-vector splitting for the Euler equations

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


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).


Mach Number Euler Equation Contact Discontinuity Shock Structure Steady Solution 
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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

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

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