Editorial Type:
Article
Article Type:
Research Article

Explicit Two-Step Peer Methods for the Compressible Euler Equations

Stefan Jebens Leibniz Institute for Tropospheric Research, Leipzig, Germany

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Oswald Knoth Leibniz Institute for Tropospheric Research, Leipzig, Germany

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Rüdiger Weiner Institute of Mathematics, University of Halle, Halle, Germany

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Print Publication:
01 Jul 2009
DOI:
https://doi.org/10.1175/2008MWR2671.1
Page(s):
2380–2392
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Abstract

A new time-splitting method for the integration of the compressible Euler equations is presented. It is based on a two-step peer method, which is a general linear method with second-order accuracy in every stage. The scheme uses a computationally very efficient forward–backward scheme for the integration of the high-frequency acoustic modes. With this splitting approach it is possible to stably integrate the compressible Euler equations without any artificial damping. The peer method is tested with the dry Euler equations and a comparison with the common split-explicit second-order three-stage Runge–Kutta method by Wicker and Skamarock shows the potential of the class of peer methods with respect to computational efficiency, stability, and accuracy.

Corresponding author address: Stefan Jebens, Leibniz Institute for Tropospheric Research, Permoserstr. 15, D-04318 Leipzig, Germany. Email: jebens@tropos.de

Abstract

A new time-splitting method for the integration of the compressible Euler equations is presented. It is based on a two-step peer method, which is a general linear method with second-order accuracy in every stage. The scheme uses a computationally very efficient forward–backward scheme for the integration of the high-frequency acoustic modes. With this splitting approach it is possible to stably integrate the compressible Euler equations without any artificial damping. The peer method is tested with the dry Euler equations and a comparison with the common split-explicit second-order three-stage Runge–Kutta method by Wicker and Skamarock shows the potential of the class of peer methods with respect to computational efficiency, stability, and accuracy.

Corresponding author address: Stefan Jebens, Leibniz Institute for Tropospheric Research, Permoserstr. 15, D-04318 Leipzig, Germany. Email: jebens@tropos.de

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