Utilizing a Mixed Implicit-Explicit Method for Solving Radiation Hydrodynamics Equations

In this article, the accuracy of two mixed explicit–implicit schemes for simulating non relativistic, radiative hydrodynamic phenomenon in the equilibrium diffusion limit is compared. In mixed explicit implicit schemes, the radiation hydrodynamics equations are solved in two stages. In the first stage (the hydrodynamics stage) a finite-volume Godunov type method is utilized. In the second stage (the radiation stage), two diffrenrt methods are used. In the first method, a linearized non-iterative implicit technique is used. In the second method, a Jacobian-free Newton–Krylov procedure is used to solve the diffusion (radiation) equation. Several examples are considered to demonstrate the accuracy and convergence properties of the two schemes used. Numerical results indicate that, the second method is more accurate. However this method is much more time consuming.