A module for radiation hydrodynamic calculations with ZEUS-2D using flux-limited diffusion

A module for the ZEUS-2D code is described that may be used to solve the equations of radiation hydrodynamics to order unity in v/c, in the flux-limited diffusion (FLD) approximation. In this approximation, the factor Eddington tensor f, which closes the radiation moment equations, is chosen to be an empirical function of the radiation energy density. This is easier to implement and faster than full-transport techniques, in which f is computed by solving the transfer equation. However, FLD is less accurate when the flux has a component perpendicular to the gradient in radiation energy density and in optically thin regions when the radiation field depends strongly on angle. The material component of the fluid is here assumed to be in local thermodynamic equilibrium. The energy equations are operator split, with transport terms, radiation diffusion term, and other source terms evolved separately. Transport terms are applied using the same consistent transport algorithm as in ZEUS-2D. The radiation diffusion term is updated using an alternating direction-implicit method with convergence checking. Remaining source terms are advanced together implicitly using numerical root finding. However, when absorption opacity is zero, accuracy is improved by instead treating the compression and expansion source terms using a time-centered differencing scheme. Results are discussed for test problems including radiation-damped linear waves, radiation fronts propagating in optically thin media, subcritical and supercritical radiating shocks, and an optically thick shock in which radiation dominates downstream pressure.