Manufactured solutions for the P1 radiation-hydrodynamics equations

For the purposes of testing numerical methods, we develop two manufactured solutions to the P1 radiation-hydrodynamics system. One solution is designed to test numerical methods in the equilibrium diffusion limit, while the other solution is valid in the streaming (small absorption) regime. We then use these solutions to test a discontinuous Galerkin (DG) discretization of the radiation-hydrodynamics system. We demonstrate that DG with linear elements, with either the double minmod slope limiter or no limiter, is second-order accurate and preserves the equilibrium diffusion limit. On the other hand, DG fails to obtain the equilibrium diffusion limit for the step method (i.e., DG with piecewise constant elements), or with linear elements using the minmod limiter. We also show that when the relativistic terms are lagged at the previous time step, the DG method converges at a first-order rate in the streaming regime for both piecewise constant and linear elements.