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TVD‐based Finite Volume Methods for Sound‐Advection‐Buyancy Systems
Author(s) -
Knoth Oswald,
Naumann Andreas,
Wensch Jörg
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410416
Subject(s) - total variation diminishing , runge–kutta methods , infinitesimal , advection , stability (learning theory) , finite volume method , mathematics , computer science , mathematical analysis , mechanics , physics , numerical analysis , thermodynamics , machine learning
Split‐explicit Runge‐Kutta methods provide an efficient integration procedure for hyperbolic systems with coupled slow and fast wave phenomena. They are generalized to multirate infinitesimal step methods (MIS) in order to develop an order to provide order conditions and to establish stability properties. The construction of MIS methods is based on an underlying Runge‐Kutta method. This method is choosen to be total variation diminishing (TVD) to improve the stability properties of the method. Here, the maximum Courant number is improved by a factor of 4. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)