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Title: A hybrid Godunov method for radiation hydrodynamics

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 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 stepmore » 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.« less

Authors:
 [1];  [1];  [2]
  1. Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544 (United States)
  2. (United States)
Publication Date:
OSTI Identifier:
21417245
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 229; Journal 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.
Country of Publication:
United States
Language:
English
Subject:
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

Citation Formats

Sekora, Michael D., E-mail: sekora@math.princeton.ed, Stone, James M., and Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544. A hybrid Godunov method for radiation hydrodynamics. United States: N. p., 2010. Web. doi:10.1016/j.jcp.2010.05.024.
Sekora, Michael D., E-mail: sekora@math.princeton.ed, Stone, James M., & Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544. A hybrid Godunov method for radiation hydrodynamics. United States. doi:10.1016/j.jcp.2010.05.024.
Sekora, Michael D., E-mail: sekora@math.princeton.ed, Stone, James M., and Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544. 2010. "A hybrid Godunov method for radiation hydrodynamics". United States. doi:10.1016/j.jcp.2010.05.024.
@article{osti_21417245,
title = {A hybrid Godunov method for radiation hydrodynamics},
author = {Sekora, Michael D., E-mail: sekora@math.princeton.ed and Stone, James M. and Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544},
abstractNote = {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.},
doi = {10.1016/j.jcp.2010.05.024},
journal = {Journal of Computational Physics},
number = 19,
volume = 229,
place = {United States},
year = 2010,
month = 9
}
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