A hybrid Godunov method for radiation hydrodynamics

JOURNAL OF COMPUTATIONAL PHYSICS

卷:229

Article

Sekora, Michael D.¹  Stone, James M.^1,2 

[1] Princeton Univ, Program Appl & Computat Math, Princeton, NJ 08544 USA

[2] Princeton Univ, Dept Astrophys Sci, Princeton, NJ 08544 USA

关键词: Godunov method;    Radiation hydrodynamics;    Asymptotic preserving;   

DOI  :  10.1016/j.jcp.2010.05.024

来源: Elsevier

【 摘 要 】

From a mathematical perspective, radiation hydrodynamics can be thought of as a system of hyperbolic balance laws with dual multiscale behavior (multiscale behavior associated with the hyperbolic wave speeds as well as multiscale behavior associated with source term relaxation). With this outlook in mind, this paper presents a hybrid Godunov method for one-dimensional radiation hydrodynamics that is uniformly well behaved from the photon free streaming (hyperbolic) limit through the weak equilibrium diffusion (parabolic) limit and to the strong equilibrium diffusion (hyperbolic) limit. Moreover, one finds that the technique preserves certain asymptotic limits. The method incorporates a backward Euler upwinding scheme for the radiation energy density E(r) and flux F(r) as well as a modified Godunov scheme for the material density rho, momentum density m, and energy density E. The backward Euler upwinding scheme is first-order accurate and uses an implicit HLLE flux function to temporally advance the radiation components according to the material flow scale. The modified Godunov scheme is second-order accurate and directly couples stiff source term effects to the hyperbolic structure of the system of balance laws. This Godunov technique is composed of a predictor step that is based on Duhamel's principle and a corrector step that is based on Picard iteration. The Godunov scheme is explicit on the material flow scale but is unsplit and fully couples matter and radiation without invoking a diffusion-type approximation for radiation hydrodynamics. This technique derives from earlier work by Miniati and Colella (2007) [41]. Numerical tests demonstrate that the method is stable, robust, and accurate across various parameter regimes. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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