A minimum entropy principle of high order schemes for gas dynamics equations
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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.
Date issued
2011-12Department
Massachusetts Institute of Technology. Department of MathematicsJournal
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
ISSN
0029-599X
0945-3245