A minimum entropy principle of high order schemes for gas dynamics equations
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...
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| Format: | Article |
| Language: | en_US |
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Springer-Verlag
2014
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| Online Access: | http://hdl.handle.net/1721.1/85657 |
| _version_ | 1811070012070297600 |
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| author | Zhang, Xiangxiong Shu, Chi-Wang |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Zhang, Xiangxiong Shu, Chi-Wang |
| author_sort | Zhang, Xiangxiong |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T08:20:46Z |
| format | Article |
| id | mit-1721.1/85657 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T08:20:46Z |
| publishDate | 2014 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | mit-1721.1/856572022-09-30T09:06:39Z A minimum entropy principle of high order schemes for gas dynamics equations Zhang, Xiangxiong Shu, Chi-Wang Massachusetts Institute of Technology. Department of Mathematics Zhang, Xiangxiong Zhang, Xiangxiong 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. United States. Air Force Office of Scientific Research (Grant FA9550-09-1-0126) National Science Foundation (U.S.) (Grant DMS-1112700) 2014-03-14T20:07:58Z 2014-03-14T20:07:58Z 2011-12 2011-09 Article http://purl.org/eprint/type/JournalArticle 0029-599X 0945-3245 http://hdl.handle.net/1721.1/85657 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. en_US http://dx.doi.org/10.1007/s00211-011-0443-7 Numerische Mathematik 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. application/pdf Springer-Verlag Zhang |
| spellingShingle | Zhang, Xiangxiong Shu, Chi-Wang A minimum entropy principle of high order schemes for gas dynamics equations |
| title | A minimum entropy principle of high order schemes for gas dynamics equations |
| title_full | A minimum entropy principle of high order schemes for gas dynamics equations |
| title_fullStr | A minimum entropy principle of high order schemes for gas dynamics equations |
| title_full_unstemmed | A minimum entropy principle of high order schemes for gas dynamics equations |
| title_short | A minimum entropy principle of high order schemes for gas dynamics equations |
| title_sort | minimum entropy principle of high order schemes for gas dynamics equations |
| url | http://hdl.handle.net/1721.1/85657 |
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