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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Research supported by AFOSR grant FA9550-09-1-0126 and NSF grant DMS-1112700.
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Zhang, X., Shu, CW. A minimum entropy principle of high order schemes for gas dynamics equations. Numer. Math. 121, 545–563 (2012). https://doi.org/10.1007/s00211-011-0443-7
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DOI: https://doi.org/10.1007/s00211-011-0443-7