Well-Balanced High Order 1D Schemes on Non-uniform Grids and Entropy Residuals

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• 作者：G. Puppo ; M. Semplice
• 关键词：High order finite volumes ; Non ; uniform grids ; Entropy ; Well balancing ; 65M08 ; 76M12
• 刊名：Journal of Scientific Computing
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：66
• 期：3
• 页码：1052-1076
• 全文大小：1,290 KB
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• 作者单位：G. Puppo (1)
  M. Semplice (2)
  
  1. Dipartimento di Scienza e Alta Tecnologia, Università dell’Insubria, Via Valleggio, 11, 22100, Como, Italy
  2. Dipartimento di Matematica “G. Peano”, Università di Torino, Via C. Alberto, 10, 10123, Turin, Italy
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algorithms
  Computational Mathematics and Numerical Analysis
  Applied Mathematics and Computational Methods of Engineering
  Mathematical and Computational Physics
  
• 出版者：Springer Netherlands
• ISSN：1573-7691

文摘

This paper is concerned with the construction of high order schemes on irregular grids for balance laws, including a discussion of an a-posteriori error indicator based on the numerical entropy production. We also impose well-balancing on non uniform grids for the shallow water equations, which can be extended similarly to other balance laws, obtaining schemes up to fourth order of accuracy with very weak assumptions on the regularity of the grid. Our results show the expected convergence rates, the correct propagation of shocks across grid discontinuities and demonstrate the improved resolution achieved with a locally refined non-uniform grid. The schemes proposed in this work naturally can also be applied to systems of conservation laws. They may also be extended to higher space dimensions by means of dimensional splitting. The error indicator based on the numerical entropy production, previously introduced for the case of systems of conservation laws, is extended to balance laws. Its decay rate and its ability to identify discontinuities is illustrated on several tests. Keywords High order finite volumes Non-uniform grids Entropy Well balancing