Asymptotic diffusion limit of cell temperature discretisation schemes for thermal radiation transport

This paper attempts to unify the asymptotic diffusion limit analysis of thermal radiation transport schemes, for a linear-discontinuous representation of the material temperature reconstructed from cell centred temperature unknowns, in a process known as ‘source tilting’. The asymptotic limits of both Monte Carlo (continuous in space) and deterministic approaches (based on linear-discontinuous finite elements) for solving the transport equation are investigated in slab geometry. The resulting discrete diffusion equations are found to have nonphysical terms that are proportional to any cell-edge discontinuity in the temperature representation. Based on this analysis it is possible to design accurate schemes for representing the material temperature, for coupling thermal radiation transport codes to a cell centred representation of internal energy favoured by ALE (arbitrary Lagrange–Eulerian) hydrodynamics schemes.