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MUSTA schemes for multi-dimensional hyperbolic systems: analysis and improvements. (English) Zbl 1073.65553
Summary: 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.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76N15 Gas dynamics, general
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
76M20 Finite difference methods applied to problems in fluid mechanics
35L65 Hyperbolic conservation laws
Software:
HE-E1GODF; MUSTA
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