Flux-vector splitting for the Euler equations

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).

Research was supported under NASA Contract No. NAS1-15810 while the author was in residence at ICASE, NASA Langley Research Center, Hampton, VA 23665.