期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 230, 期 4, 页码 1238-1248出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2010.10.036
关键词
Hyperbolic conservation laws; Discontinuous Galerkin method; Positivity preserving; High order accuracy; Compressible Euler equations with source terms; Gas dynamics; Finite volume scheme; Essentially non-oscillatory scheme; Weighted essentially non-oscillatory scheme
资金
- AFOSR [FA9550-09-1-0126]
- NSF [DMS-0809086]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0809086] Funding Source: National Science Foundation
In [16,17], we constructed uniformly high order accurate discontinuous Galerkin (DG) schemes which preserve positivity of density and pressure for the Euler equations of compressible gas dynamics with the ideal gas equation of state. The technique also applies to high order accurate finite volume schemes. For the Euler equations with various source terms (e.g., gravity and chemical reactions), it is more difficult to design high order schemes which do not produce negative density or pressure. In this paper, we first show that our framework to construct positivity-preserving high order schemes in [16,17] can also be applied to Euler equations with a general equation of state. Then we discuss an extension to Euler equations with source terms. Numerical tests of the third order Runge-Kutta DG (RKDG) method for Euler equations with different types of source terms are reported. (C) 2010 Elsevier Inc. All rights reserved.
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