Positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations with source terms

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 sc...

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Bibliographic Details
Published in:Journal of computational physics 2011-02, Vol.230 (4), p.1238-1248
Main Authors: Zhang, Xiangxiong, Shu, Chi-Wang
Format: Article
Language:English
Subjects:
Chemical reactions
Compressible Euler equations with source terms
Computational techniques
Construction
Density
Discontinuous Galerkin method
Equations of state
Essentially non-oscillatory scheme
Euler equations
Exact sciences and technology
Finite volume scheme
Galerkin methods
Gas dynamics
High order accuracy
Hyperbolic conservation laws
Mathematical analysis
Mathematical methods in physics
Physics
Positivity preserving
Preserves
Runge-Kutta method
Weighted essentially non-oscillatory scheme
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Summary: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.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2010.10.036