Multidimensional upwind methods for hyperbolic conservation laws. (English) Zbl 0694.65041

A class of conservative difference algorithms for hyperbolic conservation laws in several space variables which do not make use of operator splitting are presented. These methods are upwind and multidimensional, in that the numerical fluxes are obtained by solving the characteristic form of the full multidimensional equations at the zone edge and that all fluxes are evaluated and differenced at the same time.
The correct behavior at the discontinuities is obtained by use of solutions to the Riemann problem and by limiting some of the second-order terms. Numerical experiments show that the methods described here yield the same high resolution as the corresponding operator split methods.
Reviewer: V.A.Kostova


65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
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