On the optimal CFL number of SSP methods for hyperbolic problems

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Date

2019-01-01

Authors

Giuliani, Andrew
Krivodonova, Lilia

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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.

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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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