TY - JOUR
T1 - A higher-order Godunov method for radiation hydrodynamics
T2 - Radiation subsystem
AU - Sekora, Michael David
AU - Stone, James McLellan
N1 - Funding Information:
The authors thank Dr. Phillip Colella for many helpful discussions. MS acknowledges support from the DOE CSGF Program which is provided under grant DE-FG02-97ER25308. JS acknowledges support from grant DE-FG52-06NA26217.
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
KW - Asymptotic preserving methods
KW - Godunov methods
KW - Hyperbolic conservation laws
KW - Radiation hydrodynamics
KW - Stiff relaxation
KW - Stiff source terms
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U2 - 10.2140/camcos.2009.4.135
DO - 10.2140/camcos.2009.4.135
M3 - Article
AN - SCOPUS:85015386113
VL - 4
SP - 135
EP - 152
JO - Communications in Applied Mathematics and Computational Science
JF - Communications in Applied Mathematics and Computational Science
SN - 1559-3940
IS - 1
ER -