Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes
Journal of Computational Physics
Multidimensional upwind methods for hyperbolic conservation laws
Journal of Computational Physics
Numerical schemes for hyperbolic conservation laws with stiff relaxation terms
Journal of Computational Physics
Numerical simulations for radiation hydrodynamics. I. diffusion limit
Journal of Computational Physics
Numerical simulations for radiation hydrodynamics: II. transport limit
Journal of Computational Physics
ADER: Arbitrary High Order Godunov Approach
Journal of Scientific Computing
Asymptotic preserving and positive schemes for radiation hydrodynamics
Journal of Computational Physics
A modified higher order Godunov's scheme for stiff source conservative hydrodynamics
Journal of Computational Physics
SIAM Journal on Scientific Computing
Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws
Journal of Computational Physics
Short Note: A limiter for PPM that preserves accuracy at smooth extrema
Journal of Computational Physics
Journal of Computational Physics
Self-consistent solution of cosmological radiation-hydrodynamics and chemical ionization
Journal of Computational Physics
Very high order PNPM schemes on unstructured meshes for the resistive relativistic MHD equations
Journal of Computational Physics
A stable and convergent scheme for viscoelastic flow in contraction channels
Journal of Computational Physics
Hi-index | 31.45 |
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"r and flux F"r as well as a modified Godunov scheme for the material density @r, 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) [41]. Numerical tests demonstrate that the method is stable, robust, and accurate across various parameter regimes.