The NIKE Code: A Hybrid Godunov Method for Radiation Hydrodynamics

Michael Sekora, Princeton University

Photo of Michael Sekora

Radiation hydrodynamics is a fluid description of matter (plasma) that absorbs and emits electromagnetic radiation and in so doing modifies dynamical behavior. The coupling between matter and radiation is significant in many phenomena related to astrophysics and plasma physics, where radiation comprises a major fraction of the system’s internal energy and momentum and provides the dominant transport mechanism. Our research focuses on a numerical method that we have been developing for radiation hydrodynamics (i.e., conservation laws with stiff source terms) that is asymptotically preserving and uniformly well behaved from the free streaming (hyperbolic) limit through the equilibrium diffusion (parabolic) limit and to the strong diffusion (hyperbolic) limit.

The algorithm presented here is a hybrid method that incorporates a backward Euler upwinding scheme for the radiation components and a modified Godunov scheme for the material components. The backward Euler scheme is a 1st order accurate technique that uses an implicit HLLE flux function to temporally advance the radiation components according to the material flow scale. The modified Godunov scheme is a 2nd order accurate technique that directly couples stiff source term effects to the hyperbolic structure of the system of conservation laws. The modified Godunov method 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 source terms without invoking a diffusion-type approximation.

Abstract Author(s): Michael Sekora, James Stone