1990•NASA STI Repository (National Aeronautics and Space Administration)Open access

Towards a genuinely multi-dimensional upwind scheme

Kenneth G. Powell, Bram Vanleer, Philip L. Roe

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.

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Key concepts: Upwind scheme, Riemann solver, Roe solver, Scheme (mathematics), Solver, Riemann hypothesis, Applied mathematics, Riemann problem