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High resolution finite volume methods on arbitrary grids via wave propagation. (English) Zbl 0649.65050
One generalization of Godunov’s method for systems of conservation laws developed in the author’s previous work is extended to second-order accuracy and to a two-dimensional finite volume method, which avoids the usual time-step restriction of explicit method by virtue of solving one- dimensional normal and tangential Riemannian problems and of propagating waves through one or more mesh cells, and makes it possible to use reasonable time steps on irregular grids. The author considers boundary conditions for the Euler equations and pays special attention to the case of a Cartesian grid cut by an irregular boundary. The corresponding numerical results are analyzed.
Reviewer: V.Kamen

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
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