Explicit Two-Step Peer Methods for the Compressible Euler Equations | Zendy

Stefan Jebens | Zendy; Oswald Knoth | Zendy; Rüdiger Weiner | Zendy

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Explicit Two-Step Peer Methods for the Compressible Euler Equations

Author(s) -

Stefan Jebens,

Oswald Knoth,

Rüdiger Weiner

Publication year - 2009

Publication title -

monthly weather review

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.862

H-Index - 179

eISSN - 1520-0493

pISSN - 0027-0644

DOI - 10.1175/2008mwr2671.1

Subject(s) - euler equations , backward euler method , runge–kutta methods , semi implicit euler method , euler method , euler's formula , compressible flow , compressibility , scheme (mathematics) , mathematics , stability (learning theory) , computer science , mathematical analysis , numerical analysis , mechanics , physics , machine learning

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 integrate stably 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.

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