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Abstract
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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.
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Keywords
Godunov methods, radiation hydrodynamics,
asymptotic preserving methods, hyperbolic conservation laws,
stiff source terms, stiff relaxation
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Mathematical Subject Classification
Primary: 35B40, 35L65, 35M10, 76M12
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Milestones
Received: 18 February 2008
Revised: 28 November 2008
Accepted: 23 June 2009
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