A minimum entropy principle of high order schemes for gas dynamics equations
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Zhang_A minimum.pdf
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Author(s)
Zhang, Xiangxiong
Shu, Chi-Wang
Date Issued
December 2011
Journal
Numerische Mathematik
Publisher
Springer-Verlag
Citation
Zhang, Xiangxiong, and Chi-Wang Shu. “A Minimum Entropy Principle of High Order Schemes for Gas Dynamics Equations.” Numerische Mathematik 121, no. 3 (July 2012): 545–563.
Version
Author's final manuscript
Abstract
The entropy solutions of the compressible Euler equations satisfy a minimum principle for the specific entropy (Tadmor in Appl Numer Math 2:211–219, 1986). First order schemes such as Godunov-type and Lax-Friedrichs schemes and the second order kinetic schemes (Khobalatte and Perthame in Math Comput 62:119–131, 1994) also satisfy a discrete minimum entropy principle. In this paper, we show an extension of the positivity-preserving high order schemes for the compressible Euler equations in Zhang and Shu (J Comput Phys 229:8918–8934, 2010) and Zhang et al. (J Scientific Comput, in press), to enforce the minimum entropy principle for high order finite volume and discontinuous Galerkin (DG) schemes.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00211-011-0443-7
