Studies of deterministic transport methods for thermal radiation on unstructured meshes - 023

Numerical simulations of Inertial Confinement Fusion (ICF) and plasma physics experiments on the National Ignition Facility, require the development of thermal radiation transport methods for both the 2D and 3D unstructured meshes used by hydrodynamics codes. Due to the computational complexities inherent in solving the transport equation, a solution of the diffusion equation has been developed for these types of meshes. In combination with a flux limiting procedure this can provide reasonably accurate results for a wide class of problems. Details of this scheme are presented together with the results from example calculations of an ICF capsule implosion. The diffusion approximation is adequate for qualitative modelling of capsule performance. However accurate solutions of the transport equation are required in order to model the details of the radiation drive from the hohlraum. Ideas for extending this work to provide accurate solutions of the transport equation are considered in the remainder of the paper. Computational experiments in 1D slab geometry are used to study the performance of potential schemes based on the use of finite element methods in space and angle. Promising results are obtained for both the first and second order forms of the transport equation with the intensity as the primitive variable. (author)