期刊
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
卷 467, 期 2134, 页码 2752-2776出版社
ROYAL SOC
DOI: 10.1098/rspa.2011.0153
关键词
hyperbolic conservation laws; discontinuous Galerkin method; weighted essentially non-oscillatory finite-volume scheme; positivity-preserving; maximum-principle-satisfying; high-order accuracy
资金
- AFOSR [FA9550-09-1-0126]
- NSF [DMS-0809086]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0809086] Funding Source: National Science Foundation
In an earlier study (Zhang & Shu 2010b J. Comput. Phys. 229, 3091-3120 (doi: 10.1016/j.jcp.2009.12.030), genuinely high-order accurate finite volume and discontinuous Galerkin schemes satisfying a strict maximum principle for scalar conservation laws were developed. The main advantages of such schemes are their provable high-order accuracy and their easiness for generalization to multi-dimensions for arbitrarily high-order schemes on structured and unstructured meshes. The same idea can be used to construct high-order schemes preserving the positivity of certain physical quantities, such as density and pressure for compressible Euler equations, water height for shallow water equations and density for Vlasov-Boltzmann transport equations. These schemes have been applied in computational fluid dynamics, computational astronomy and astrophysics, plasma simulation, population models and traffic flow models. In this paper, we first review the main ideas of these maximum-principle-satisfying and positivity-preserving high-order schemes, then present a simpler implementation which will result in a significant reduction of computational cost especially for weighted essentially non-oscillatory finite-volume schemes.
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