A Parallel First-Order Spherical Harmonics (P₁) Matrix-Free Method for Radiative Transport

Abstract

Radiative transfer in participating media is modeled using a first-order spherical harmonics (P₁), or its degenerate form, diffusion. The equations are discretized on an unstructured grid. The method uses a matrix-free algorithm employing an iterative solver from the Preconditioned Conjugate Gradient (PCG) solver package developed by Joubert and Carey [1]. The algorithm couples radiation transport and conduction, by casting them into a Picard iteration. Compared are solutions for two participating media problems indicating the method to be first-order accurate in time. Parallel scaling of the matrix-free method with use of in-situ preconditioners, symmetric successive overrelaxation (SSOR) and block Jacobi, are reported.

Acknowledgments

I thank my colleagues at Los Alamos National Laboratory for their discussions and guidance regarding radiation transport and its solution. In particular, I thank Vincent Mousseau, whose suggestions were helpful in the development of the capabilities shown here. Also, I thank Scott Turner, Mark Gray, Gordon Olson, and Jim Morel: You have in large part provided for the development of the original matrix version of this P₁ method.

Los Alamos National Laboratory, an affirmative action/equal opportunity employer, is operated by the Los Alamos National Security, LLC, for the National Nuclear Security Administration of the U.S. Department of Energy under contract DE-AC52-06NA25396. Los Alamos National Laboratory strongly supports academic freedom and a researcher's right to publish; as an institution, however, the Laboratory does not endorse the viewpoint of a publication or guarantee its technical correctness. Reference: LA-UR-07-5770.