A Positive Asymptotic Preserving Scheme for Linear Kinetic Transport Equations
Abstract
We present a positive and asymptotic preserving numerical scheme for solving linear kinetic, transport equations that relax to a diffusive equation in the limit of infinite scattering. The proposed scheme is developed using a standard spectral angular discretization and a classical micro-macro decomposition. The three main ingredients are a semi-implicit temporal discretization, a dedicated finite difference spatial discretization, and realizability limiters in the angular discretization. Under mild assumptions on the initial condition and time step, the scheme becomes a consistent numerical discretization for the limiting diffusion equation when the scattering cross-section tends to infinity. The scheme also preserves positivity of the particle concentration on the space-time mesh and therefore fixes a common defect of spectral angular discretizations. The scheme is tested on the well-known line source benchmark problem with the usual uniform material medium as well as a medium composed from different materials that are arranged in a checkerboard pattern. We also report the observed order of space-time accuracy of the proposed scheme.
Keywords
Cite
@article{arxiv.1807.06109,
title = {A Positive Asymptotic Preserving Scheme for Linear Kinetic Transport Equations},
author = {M. Paul Laiu and Martin Frank and Cory D. Hauck},
journal= {arXiv preprint arXiv:1807.06109},
year = {2018}
}