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A third-order accurate wave propagation algorithm for hyperbolic partial differential equations. (English) Zbl 1476.65206

Summary: We extend LeVeque’s wave propagation algorithm, a widely used finite volume method for hyperbolic partial differential equations, to a third-order accurate method. The resulting scheme shares main properties with the original method, i.e., it is based on a wave decomposition at grid cell interfaces, it can be used to approximate hyperbolic problems in divergence form as well as in quasilinear form and limiting is introduced in the form of a wave limiter.

MSC:

65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
76M12 Finite volume methods applied to problems in fluid mechanics
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