Vol. 4, No. 1, 2009

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ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
A higher-order Godunov method for radiation hydrodynamics: Radiation subsystem

Michael David Sekora and James M. Stone

Vol. 4 (2009), No. 1, 135–152
Abstract

A higher-order Godunov method for the radiation subsystem of radiation hydrodynamics is presented. A key ingredient of the method is the direct coupling of stiff source term effects to the hyperbolic structure of the system of conservation laws; it is composed of a predictor step that is based on Duhamel’s principle and a corrector step that is based on Picard iteration. The method is second-order accurate in both time and space, unsplit, asymptotically preserving, and 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. Numerical tests demonstrate second-order convergence across various parameter regimes.

Keywords
Godunov methods, radiation hydrodynamics, asymptotic preserving methods, hyperbolic conservation laws, stiff source terms, stiff relaxation
Mathematical Subject Classification 2000
Primary: 35B40, 35L65, 35M10, 76M12
Milestones
Received: 18 February 2008
Revised: 28 November 2008
Accepted: 23 June 2009
Published: 2 October 2009
Authors
Michael David Sekora
Program in Applied and Computational Mathematics
Princeton University
Princeton, NJ 08540
United States
James M. Stone
Department of Astrophysical Sciences
Princeton University
Princeton, NJ 08540
United States