Speaker: Ming Tse Paul Laiu, Oak Ridge National Laboratory

Title: A Positive Asymptotic Preserving Scheme for Linear Kinetic Transport Equations

Date: 12/07/2018

Time: 4:10 PM - 5:00 PM

Place: 1502 Engineering Building

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 and gives promising results.