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

• Published in: International journal for numerical methods in fluids Vol. 49; no. 2; pp. 117 - 147
• Main Authors: Titarev, V. A., Toro, E. F.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 20-09-2005; Wiley
• Subjects: Compressible flows; shock and detonation phenomena; Computational methods in fluid dynamics; Exact sciences and technology; Fluid dynamics; FORCE flux; Fundamental areas of phenomenology (including applications); MUSTA flux; Physics; Riemann solver; Shock-wave interactions and shock effects; Shock-wave interactions and shockeffects; stability in multiple space dimensions; Compressible fluid; Hyperbolic system; Computational fluid dynamics; Riemann problem; Gas dynamics; Digital simulation; stability in multiple space dimensions; Euler equations; MUSTA flux; Upwind scheme; Shock waves; Mach reflection; Blast wave; FORCE flux; Monotonicity; Riemann solver
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.980

We develop and analyse an improved version of the multi‐stage (MUSTA) approach to the construction of upwind Godunov‐type fluxes 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 technology into the framework of finite‐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.