MUSTA schemes for multi‐dimensional hyperbolic systems: analysis and improvements

SUMMARY We develop and analyse an improved version of the multi-stage (MUSTA) approach to the construction of upwind Godunov-typeuxes whereby the solution of the Riemann problem, approximate or exact, is not required. The new MUSTA schemes improve upon the original schemes in terms of monotonicity properties, accuracy and stability in multiple space dimensions. We incorporate the MUSTA technol- ogy into the framework ofnite-volume weighted essentially nonoscillatory schemes as applied to the Euler equations of compressible gas dynamics. The results demonstrate that our new schemes are good alternatives to current centred methods and to conventional upwind methods as applied to complicated hyperbolic systems for which the solution of the Riemann problem is costly or unknown. Copyright ? 2005 John Wiley & Sons, Ltd.