Universität zu Köln

Derigs, Dominik, Gassner, Gregor J., Walch, Stefanie and Winters, Andrew R. (2019). Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics. Technical Report.

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Abstract

This article serves as a summary outlining the mathematical entropy analysis of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD equations as they are particularly useful for mathematically modeling a wide variety of magnetized fluids. In order to be self-contained we first motivate the physical properties of a magnetic fluid and how it should behave under the laws of thermodynamics. Next, we introduce a mathematical model built from hyperbolic partial differential equations (PDEs) that translate physical laws into mathematical equations. After an overview of the continuous analysis, we thoroughly describe the derivation of a numerical approximation of the ideal MHD system that remains consistent to the continuous thermodynamic principles. The derivation of the method and the theorems contained within serve as the bulk of the review article. We demonstrate that the derived numerical approximation retains the correct entropic properties of the continuous model and show its applicability to a variety of standard numerical test cases for MHD schemes. We close with our conclusions and a brief discussion on future work in the area of entropy consistent numerical methods and the modeling of plasmas.

Item Type:	Monograph (Technical Report)
Creators:	Creators Email ORCID ORCID Put Code Derigs, Dominik UNSPECIFIED UNSPECIFIED UNSPECIFIED Gassner, Gregor J. UNSPECIFIED UNSPECIFIED UNSPECIFIED Walch, Stefanie UNSPECIFIED UNSPECIFIED UNSPECIFIED Winters, Andrew R. awinters@math.uni-koeln.de UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-92719
Series Name at the University of Cologne:	Technical report series. Center for Data and Simulation Science
Volume:	2019,2
Date:	25 January 2019
Language:	English
Faculty:	Central Institutions / Interdisciplinary Research Centers
Divisions:	Weitere Institute, Arbeits- und Forschungsgruppen > Center for Data and Simulation Science (CDS)
Subjects:	Data processing Computer science Mathematics Technology (Applied sciences)
Uncontrolled Keywords:	Keywords Language Computational physics English Entropy conservation English Entropy stability English Ideal MHD equations English Finite volume methods English
URI:	http://kups.ub.uni-koeln.de/id/eprint/9271