A hybrid Godunov method for radiation hydrodynamics

Michael D. Sekora, James McLellan Stone

Research output: Contribution to journalArticle

19 Scopus citations

Abstract

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 Er and flux Fr as well as a modified Godunov scheme for the material density ρ, 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.

Original languageEnglish (US)
Pages (from-to)6819-6852
Number of pages34
JournalJournal of Computational Physics
Volume229
Issue number19
DOIs
StatePublished - Jan 1 2010

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Asymptotic preserving
  • Godunov method
  • Radiation hydrodynamics

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