Semi-implicit front capturing schemes for the degenerate nonlinear radiative diffusion equation

Nonlinear radiative diffusion equation is coupled with fluid equations or magnetic hydrodynamical equations in radiation hydrodynamics simulations. The time scales of radiation and fluid can be different. To use the same time step in the coupled system, one needs to design numerical schemes for the nonlinear radiative diffusion equation that are stable for large time steps. Due to the nonlinearity and degeneracy, fully implicit schemes may exhibit time step constraints. We propose and test two different semi implicit schemes in this paper. One allows for a hyperbolic CFL condition, and only one linear diffusion system and a scalar forth order polynomial on each space grid have to be solved implicitly in each time step. The other has a much larger CFL number, but a nonlinear system has to be solved in each time step. Though the computational cost of the second scheme in each time step is higher, the overall computational cost can be lower. Extensive numerical examples for both smooth and compactly supported solutions are presented to show the accuracy and stability of the schemes. (c) 2021 Elsevier Inc. All rights reserved. <comment>Superscript/Subscript Available</comment