Second order time evolution of the multigroup diffusion and P1 equations for radiation transport

An existing solution method for solving the multigroup radiation equations, linear multifrequency-grey acceleration, is here extended to be second order in time. This method works for simple diffusion and for flux-limited diffusion, with or without material conduction. A new method is developed that does not require the solution of an averaged grey transport equation. It is effective solving both the diffusion and P1 forms of the transport equation. Two dimensional, multi-material test problems are used to compare the solution methods.

► An existing multigroup transport algorithm is extended to be second-order in time.
► A new algorithm is presented that does not require a grey acceleration solution.
► The two algorithms are tested with 2D, multi-material problems.
► The two algorithms have comparable computational requirements.