A Third-Order Accurate Wave Propagation Algorithm for Hyperbolic Partial Diferential Equations

doi:10.1007/s42967-019-00056-3

Communications on Applied Mathematics and Computation ›› 2020, Vol. 2 ›› Issue (3): 403-427.doi: 10.1007/s42967-019-00056-3

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A Third-Order Accurate Wave Propagation Algorithm for Hyperbolic Partial Diferential Equations

Christiane Helzel

Institute of Mathematics, Heinrich-Heine-University Düsseldorf, Düsseldorf, Germany

收稿日期:2019-04-16 修回日期:2019-09-29 出版日期:2020-09-20 发布日期:2020-05-12
通讯作者: Christiane Helzel E-mail:christiane.helzel@hhu.de

A Third-Order Accurate Wave Propagation Algorithm for Hyperbolic Partial Diferential Equations

Christiane Helzel

Institute of Mathematics, Heinrich-Heine-University Düsseldorf, Düsseldorf, Germany

Received:2019-04-16 Revised:2019-09-29 Online:2020-09-20 Published:2020-05-12
Contact: Christiane Helzel E-mail:christiane.helzel@hhu.de

摘要/Abstract

摘要： We extend LeVeque’s wave propagation algorithm, a widely used fnite volume method for hyperbolic partial diferential 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.

关键词: Wave propagation algorithm, Hyperbolic partial diferential equations, Thirdorder accuracy

Abstract: We extend LeVeque’s wave propagation algorithm, a widely used fnite volume method for hyperbolic partial diferential 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.

Key words: Wave propagation algorithm, Hyperbolic partial diferential equations, Thirdorder accuracy

中图分类号:

65M08
76M12

Christiane Helzel. A Third-Order Accurate Wave Propagation Algorithm for Hyperbolic Partial Diferential Equations[J]. Communications on Applied Mathematics and Computation, 2020, 2(3): 403-427.

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A Third-Order Accurate Wave Propagation Algorithm for Hyperbolic Partial Diferential Equations

A Third-Order Accurate Wave Propagation Algorithm for Hyperbolic Partial Diferential Equations

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