Flux-vector splitting for the Euler equations
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  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. ,  (one-dimensional) and , r91 (two-dimensional).
KeywordsMach Number Euler Equation Contact Discontinuity Shock Structure Steady Solution
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