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Erschienen in: Journal of Scientific Computing 3/2016

27.01.2016

Explicit Strong Stability Preserving Multistage Two-Derivative Time-Stepping Schemes

verfasst von: Andrew J. Christlieb, Sigal Gottlieb, Zachary Grant, David C. Seal

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2016

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Abstract

High order strong stability preserving (SSP) time discretizations are advantageous for use with spatial discretizations with nonlinear stability properties for the solution of hyperbolic PDEs. The search for high order strong stability time-stepping methods with large allowable strong stability time-step has been an active area of research over the last two decades. Recently, multiderivative time-stepping methods have been implemented with hyperbolic PDEs. In this work we describe sufficient conditions for a two-derivative multistage method to be SSP, and find some optimal SSP multistage two-derivative methods. While explicit SSP Runge–Kutta methods exist only up to fourth order, we show that this order barrier is broken for explicit multi-stage two-derivative methods by designing a three stage fifth order SSP method. These methods are tested on simple scalar PDEs to verify the order of convergence, and demonstrate the need for the SSP condition and the sharpness of the SSP time-step in many cases.

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Metadaten
Titel
Explicit Strong Stability Preserving Multistage Two-Derivative Time-Stepping Schemes
verfasst von
Andrew J. Christlieb
Sigal Gottlieb
Zachary Grant
David C. Seal
Publikationsdatum
27.01.2016
Verlag
Springer US
Erschienen in
Journal of Scientific Computing / Ausgabe 3/2016
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-016-0164-2

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