DG-IMEX method for a two-moment model for radiation transport in the $\mathscr{O}$($v$/$c$) limit

Laiu, M. Paul; Endeve, Eirik; Harris, J. Austin; Elledge, Zachary; Mezzacappa, Anthony

doi:10.1016/j.jcp.2024.113477

DG-IMEX method for a two-moment model for radiation transport in the $$\mathscr{O}$$($$v$$/$$c$) limit

Journal Article · Thu Oct 03 00:00:00 EDT 2024 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2024.113477· OSTI ID:2538479

Laiu, M. Paul ^[1]; ^[2]; Harris, J. Austin ^[1]; ^[3]; Mezzacappa, Anthony ^[3]

Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States); University of Tennessee Knoxville, TN (United States)
University of Tennessee Knoxville, TN (United States)

Here, we consider neutral 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 $$\mathscr{O}$$($$v$$/$$c$), expresses a balance between phase-space advection and collisions and includes velocity-dependent terms that account for spatial advection, Doppler shift, and angular aberration. The model is conservative for the correct $$\mathscr{O}$$($$v$$/$$c$) Eulerian-frame number density and is consistent, to $$\mathscr{O}$$($$v$$/$$c$), with Eulerian-frame energy and momentum conservation. This model is closely related to the one promoted by Lowrie et al. and similar to models currently used to study transport phenomena in large-scale simulations of astrophysical environments. The proposed numerical 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 uxes; (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 global convergence. We also analyze the simultaneous Eulerian-frame number and energy conservation properties of the semi-discrete DG scheme and propose a "spectral redistribution" scheme 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.

View Accepted Manuscript (DOE)

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC); USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 2538479

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 520; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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