A hybrid Godunov method for radiation hydrodynamics

Journal Article · Mon Sep 20 00:00:00 EDT 2010 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2010.05.024· OSTI ID:21417245

Stone, James M ^[1]

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1. Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544 (United States)

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{sub r} and flux F{sub 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) . Numerical tests demonstrate that the method is stable, robust, and accurate across various parameter regimes.

• OSTI ID: 21417245
• Journal Information: Journal of Computational Physics, Vol. 229, Issue 19; Other Information: DOI: 10.1016/j.jcp.2010.05.024; PII: S0021-9991(10)00285-8; Copyright (c) 2010 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
APPROXIMATIONS
ASYMPTOTIC SOLUTIONS
BALANCES
DIFFUSION
ENERGY DENSITY
EQUILIBRIUM
FUNCTIONS
HYDRODYNAMICS
MATHEMATICAL MODELS
ONE-DIMENSIONAL CALCULATIONS
CALCULATION METHODS
FLUID MECHANICS
MATHEMATICAL SOLUTIONS
MEASURING INSTRUMENTS
MECHANICS
WEIGHT INDICATORS