Abstract
We present a realizability-preserving numerical method for solving a spectral two-moment model to simulate the transport of massless, neutral particles interacting with a steady background material moving with relativistic velocities. The model is obtained as the special relativistic limit of a four-momentum-conservative general relativistic two-moment model. Using a maximum-entropy closure, we solve for the Eulerian-frame energy and momentum. The proposed numerical method is designed to preserve moment realizability, which corresponds to moments defined by a nonnegative phase-space density. The realizability-preserving method is achieved with the following key components: (i) a discontinuous Galerkin phase-space discretization with specially constructed numerical fluxes in the spatial and energy dimensions; (ii) a strong stability-preserving implicit-explicit time-integration method; (iii) a realizability-preserving conserved to primitive moment solver; (iv) a realizability-preserving implicit collision solver; and (v) a realizability-enforcing limiter. Component (iii) is necessitated by the closure procedure, which closes higher order moments nonlinearly in terms of primitive moments. The nonlinear conserved to primitive and the implicit collision solves are formulated as fixed-point problems, which are solved with custom iterative solvers designed to preserve the realizability of each iterate. With a series of numerical tests, we demonstrate the accuracy and robustness of this discontinuous-Galerkin-implicit-explicit method.
| Original language | English |
|---|---|
| Article number | 043001 |
| Journal | Physical Review D |
| Volume | 111 |
| Issue number | 4 |
| DOIs | |
| State | Published - Feb 15 2025 |
Funding
This research was supported in part by the Exascale Computing Project (Grant No. 17-SC-20-SC), a collaborative effort of the U.S. Department of Energy (DOE) Office of Science and the National Nuclear Security Administration. E. E. acknowledges support from the National Science Foundation (NSF) Computational Mathematics program under Grant No. 2309591 and the Gravitational Physics Program under Grant No. 2110177. J. H. and Y. X. acknowledge support from the NSF Grants No. DMS-1753581 and No. DMS-2309590. This research was supported in part by an appointment with the NSF Mathematical Sciences Graduate Internship (MSGI) Program. This program is administered by the Oak Ridge Institute for Science and Education (ORISE) through an interagency agreement between the U.S. DOE and NSF. ORISE is managed for DOE by ORAU. This manuscript has been authored, in part, by UT-Battelle, LLC, under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy (DOE). This research was supported in part by the Exascale Computing Project (Grant No. 17-SC-20-SC), a collaborative effort of the U.S. Department of Energy (DOE) Office of Science and the National Nuclear Security Administration. E.E. acknowledges support from the National Science Foundation (NSF) Computational Mathematics program under Grant No. 2309591 and the Gravitational Physics Program under Grant No. 2110177. J.H. and Y.X. acknowledge support from the NSF Grants No. DMS-1753581 and No. DMS-2309590. This research was supported in part by an appointment with the NSF Mathematical Sciences Graduate Internship (MSGI) Program. This program is administered by the Oak Ridge Institute for Science and Education (ORISE) through an interagency agreement between the U.S. DOE and NSF. ORISE is managed for DOE by ORAU. This manuscript has been authored, in part, by UT-Battelle, LLC, under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy (DOE).