A Rotationally Biased Upwind Difference Scheme for the Euler Equations

The upwind difference schemes of Godunov, Osher, Roe and van Leer are able to resolve one-dimensional steady shocks for the Euler equations within one or two mesh intervals. Unfortunately, this resolution is lost in two dimensions when the shock crosses the computing grid at an oblique angle. To correct this problem, a numerical scheme is developed which automatically locates the angle at which a shock might be expected to cross the computing grid then constructs separate finite difference formulas for the flux components normal and tangential to this direction. Numerical results are presented which illustrate the ability of this new method to resolve steady oblique shocks.