Towards a genuinely multi-dimensional upwind scheme

Abstract

Methods of incorporating multi-dimensional ideas into algorithms for the solution of Euler equations are presented. Three schemes are developed and tested: a scheme based on a downwind distribution, a scheme based on a rotated Riemann solver and a scheme based on a generalized Riemann solver. The schemes show an improvement over first-order, grid-aligned upwind schemes, but the higher-order performance is less impressive. An outlook for the future of multi-dimensional upwind schemes is given