A minimum entropy principle of high order schemes for gas dynamics equations |
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Authors: | Xiangxiong Zhang Chi-Wang Shu |
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Institution: | 1. Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA 2. Department of Mathematics, MIT, Cambridge, MA, 02139, USA
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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. |
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