DG-IMEX Method for a Two-Moment Model for Radiation Transport in the 𝒪(v/c) Limit

by   M. Paul Laiu, et al.

We consider particle systems described by moments of a phase-space density and propose a realizability-preserving numerical method to evolve a spectral two-moment model for particles interacting with a background fluid moving with nonrelativistic velocities. The system of nonlinear moment equations, with special relativistic corrections to 𝒪(v/c), expresses a balance between phase-space advection and collisions and includes velocity-dependent terms that account for spatial advection, Doppler shift, and angular aberration. This model is closely related to the one promoted by Lowrie et al. (2001; JQSRT, 69, 291-304) and similar to models currently used to study transport phenomena in large-scale simulations of astrophysical environments. The method is designed to preserve moment realizability, which guarantees that the moments correspond to a nonnegative phase-space density. The realizability-preserving scheme consists of the following key components: (i) a strong stability-preserving implicit-explicit (IMEX) time-integration method; (ii) a discontinuous Galerkin (DG) phase-space discretization with carefully constructed numerical fluxes; (iii) a realizability-preserving implicit collision update; and (iv) a realizability-enforcing limiter. In time integration, nonlinearity of the moment model necessitates solution of nonlinear equations, which we formulate as fixed-point problems and solve with tailored iterative solvers that preserve moment realizability with guaranteed convergence. We also analyze the simultaneous Eulerian-frame number and energy conservation properties of the semi-discrete DG scheme and propose an "energy limiter" that promotes Eulerian-frame energy conservation. Through numerical experiments, we demonstrate the accuracy and robustness of this DG-IMEX method and investigate its Eulerian-frame energy conservation properties.


page 10

page 35

page 36


Leapfrog methods for relativistic charged-particle dynamics

A basic leapfrog integrator and its energy-preserving and variational / ...

Conservative DG Method for the Micro-Macro Decomposition of the Vlasov-Poisson-Lenard-Bernstein Model

The micro-macro (mM) decomposition approach is considered for the numeri...

Bounds-Preserving Lax-Wendroff Discontinuous Galerkin Schemes for Quadrature-Based Moment-Closure Approximations of Kinetic Models

The quadrature-based method of moments (QMOM) offers a promising class o...

A Deep Dive into the Distribution Function: Understanding Phase Space Dynamics with Continuum Vlasov-Maxwell Simulations

In collisionless and weakly collisional plasmas, the particle distributi...

The rotating rigid body model based on a non-twisting frame

This work proposes and investigates a new model of the rotating rigid bo...

An asymptotic preserving kinetic scheme for the M1 model of linear transport

Moment models with suitable closure can lead to accurate and computation...

Please sign up or login with your details

Forgot password? Click here to reset