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On the optimal CFL number of SSP methods for hyperbolic problems

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1-s2.0-S0168927418301910-main.pdf (634.73 KB)

Date

2019-01-01

Authors

Giuliani, Andrew
Krivodonova, Lilia

Journal Title

Journal ISSN

Volume Title

Publisher

Elsevier

Abstract

We show that the theory for strong stability preserving (SSP) time stepping methods employed with the method of lines-type discretizations of hyperbolic conservation laws may result in overly stringent time step restrictions. We analyze a fully discrete finite volume method with slope reconstruction and a second order SSP Runge–Kutta time integrator to show that the maximum stable time step can be increased over the SSP limit. Numerical examples indicate that this result extends to two-dimensional problems on triangular meshes.

Description

The final publication is available at Elsevier via https://dx.doi.org/10.1016/j.apnum.2018.08.015 © 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

CFL condition, Hyperbolic conservation laws, Method of lines, Stability, Strong stability preserving methods

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Citation

URI

https://dx.doi.org/10.1016/j.apnum.2018.08.015
 http://hdl.handle.net/10012/14042

Collections

Waterloo Research
Applied Mathematics