Universität zu Köln

Winters, Andrew R. and Gassner, Gregor J. (2016). An Entropy Stable Finite Volume Scheme for the Equations of Shallow Water Magnetohydrodynamics. J. Sci. Comput., 67 (2). S. 514 - 540. NEW YORK: SPRINGER/PLENUM PUBLISHERS. ISSN 1573-7691

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Abstract

In this work, we design an entropy stable, finite volume approximation for the shallow water magnetohydrodynamics (SWMHD) equations. The method is novel as we design an affordable analytical expression of the numerical interface flux function that exactly preserves the entropy, which is also the total energy for the SWMHD equations. To guarantee the discrete conservation of entropy requires a special treatment of a consistent source term for the SWMHD equations. With the goal of solving problems that may develop shocks, we determine a dissipation term to guarantee entropy stability for the numerical scheme. Numerical tests are performed to demonstrate the theoretical findings of entropy conservation and robustness.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Winters, Andrew R. UNSPECIFIED UNSPECIFIED UNSPECIFIED Gassner, Gregor J. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-277254
DOI:	10.1007/s10915-015-0092-6
Journal or Publication Title:	J. Sci. Comput.
Volume:	67
Number:	2
Page Range:	S. 514 - 540
Date:	2016
Publisher:	SPRINGER/PLENUM PUBLISHERS
Place of Publication:	NEW YORK
ISSN:	1573-7691
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language NUMERICAL VISCOSITY; CONSERVATION-LAWS; SOLAR TACHOCLINE; SYSTEMS Multiple languages Mathematics, Applied Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/27725