Realizability-Preserving DG-IMEX Method for the Two-Moment Model of Fermion Transport

Abstract

Building on the framework of Zhang \& Shu \cite{zhangShu_2010a,zhangShu_2010b}, we develop a realizability-preserving method to simulate the transport of particles (fermions) through a background material using a two-moment model that evolves the angular moments of a phase space distribution function $f$. The two-moment model is closed using algebraic moment closures; e.g., as proposed by Cernohorsky \& Bludman \cite{cernohorskyBludman_1994} and Banach \& Larecki \cite{banachLarecki_2017a}. Variations of this model have recently been used to simulate neutrino transport in nuclear astrophysics applications, including core-collapse supernovae and compact binary mergers. We employ the discontinuous Galerkin (DG) method for spatial discretization (in part to capture the asymptotic diffusion limit of the model) combined with implicit-explicit (IMEX) time integration to stably bypass short timescales induced by frequent interactions between particles and the background. Appropriate care is taken to ensure the method preserves strict algebraic bounds on the evolved moments (particle density and flux) as dictated by Pauli's exclusion principle, which demands a bounded distribution function (i.e., $f\in [0,1]$). This realizability-preserving scheme combines a suitable CFL condition, a realizability-enforcing limiter, a closure procedure based on Fermi-Dirac statistics, and an IMEX scheme whose stages can be written as a convex combination of forward Euler steps combined with a backward Euler step. Numerical results demonstrate the realizability-preserving properties of the scheme. We also demonstrate that the use of algebraic moment closures not based on Fermi-Dirac statistics can lead to unphysical moments in the context of fermion transport.

arXiv commentSubmitted to Journal of Computational Physics

References in corpus (14)

• Nodal Discontinuous Galerkin Methods on Graphics Processors
• Truncated Moment Formalism for Radiation Hydrodynamics in Numerical Relativity
• Post-merger evolution of a neutron star-black hole binary with neutrino transport
• A new multidimensional, energy-dependent two-moment transport code for neutrino-hydrodynamics
• General Relativistic Three-Dimensional Multi-Group Neutrino Radiation-Hydrodynamics Simulations of Core-Collapse Supernovae
• A Two-moment Radiation Hydrodynamics Module in Athena Using a Time-explicit Godunov Method
• High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics
• A New Spherical Harmonics Scheme for Multi-Dimensional Radiation Transport I: Static Matter Configurations
• Conservative 3+1 General Relativistic Variable Eddington Tensor Radiation Transport Equations
• Analytic Closures for M1 Neutrino Transport
• Implicit Filtered PN for High-Energy Density Thermal Radiation Transport using Discontinuous Galerkin Finite Elements
• Hyperbolic character of the angular moment equations of radiative transfer and numerical methods
• Formulation of discontinuous Galerkin methods for relativistic astrophysics
• Bound-Preserving Discontinuous Galerkin Methods for Conservative Phase Space Advection in Curvilinear Coordinates

Cited by in corpus (8)

• Flash-X, a multiphysics simulation software instrument
• A Novel Multi-Dimensional Boltzmann Neutrino Transport Scheme for Core-Collapse Supernovae
• Toward Realistic Models of Core Collapse Supernovae: A Brief Review
• A DG-IMEX method for two-moment neutrino transport: Nonlinear solvers for neutrino-matter coupling
• thornado-hydro: a discontinuous Galerkin method for supernova hydrodynamics with nuclear equations of state
• An Asymptotically-Correct Implicit-Explicit Time Integration Scheme for Finite Volume Radiation-Hydrodynamics
• Conservative DG Method for the Micro-Macro Decomposition of the Vlasov-Poisson-Lenard-Bernstein Model
• A Discontinuous Galerkin Method for General Relativistic Hydrodynamics in thornado