Oak Ridge, TN
September 6, 2018
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, 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 well-known benchmark problems with a uniform material medium as well as a medium composed from different materials that are arranged in a checkerboard pattern.
Biography: Paul Laiu is a postdoctoral researcher in the Computational and Applied Mathematics (CAM) Group at Oak Ridge National Laboratory. He received his Ph.D. degree in Electrical and Computer Engineering from the University of Maryland, College Park in 2016. He was a postdoctoral research associate at the Mathematics department in the University of Tennessee Knoxville. His research interest includes numerical optimization, approximation theory, and numerical schemes for various partial differential equations in kinetic theory.