Accurate Front Capturing Asymptotic Preserving Scheme for Nonlinear Gray Radiative Transfer Equation

We develop an asymptotic preserving scheme for the gray radiative transfer equation. Two regimes are considered: one is a diffusive regime described by nonlinear diffusion equation material temperature; other free streaming with zero opacity. To alleviate restriction on time step and capture correct front propagation in limit, implicit treatment crucial. However, this often involves large-scale iterative solver as spatial angular dimensions coupled. Our idea to introduce auxiliary variable that leads “redundant" system, which then solved three-stage update: prediction, correction, projection. The benefit of approach system local each element, independent variable, thus only requires scalar Newton's solver. also discretization compact stencil based even-odd decomposition. method preserves both limit speed hyperbolic CFL condition.