thornado-transport: IMEX schemes for two-moment neutrino transport respecting Fermi-Dirac statistics

Abstract

We develop implicit-explicit (IMEX) schemes for neutrino transport in a background material in the context of a two-moment model that evolves the angular moments of a neutrino phase-space distribution function. Considering the upper and lower bounds that are introduced by Pauli’s exclusion principle on the moments, an algebraic moment closure based on Fermi-Dirac statistics and a convex-invariant time integrator both are demanded. A finite-volume/first-order discontinuous Galerkin(DG) method is used to illustrate how an algebraic moment closure based on Fermi-Dirac statistics is needed to satisfy the bounds. Several algebraic closures are compared with these bounds in mind, and the Cernohorsky and Bludman closure, which satisfies the bounds, is chosen for our IMEX schemes. For the convex-invariant time integrator, two IMEX schemes named PD-ARS have been proposed. PD-ARS denotes a convex-invariant IMEX Runge-Kutta scheme that is high-order accurate in the streaming limit, and works well in the diffusion limit. Our two PD-ARS schemes use second-and third-order, explicit, strong-stability-preserving Runge-Kutta methods as their explicit part, respectively, and therefore are second-and third-order accurate in the streaming limit, respectively. The accuracy and convex-invariance of our PD-ARS schemes are demonstrated in the numerical tests with a third-order DG method for spatial discretization and a simple Lax-Friedrichs flux. The method has been implemented in our high-order neutrino-radiation hydrodynamics (thornado) toolkit. We show preliminary results employing tabulated neutrino opacities.

Exascale models of stellar explosions: Quintessential multi-physics simulation

“…The semi-discrete system evolved with FV methods can then be written as a system of ODEswhere u¯ represents the cell averages of the solution vector u across the computational domain, the right-hand side represents the combined FV representation of convection and gravitational terms, and Φ is the Newtonian gravitational potential. The moment equations—including the coupling between the fluid and the radiation field—are discretized with DG methods (see Chu et al (2019a, 2019b); Laiu et al (2020, 2021) for details). The semi-discrete system evolved with DG methods can be written as the following systems of ODEswhere boldu and boldM, respectively, represent all the fluid and radiation degrees of freedom evolved with the DG method.…”

“…The toolkit for high-order neutrino radiation hydrodynamics 4 (thornado) (Chu et al, 2019a(Chu et al, , 2019bEndeve et al, 2019) is being independently developed for modeling CCSNe. For ExaStar, we are interested in the capability of thornado to evolve the neutrino radiation field with spectral neutrino transport using a two-moment model, where moments of the neutrino phase-space distribution function-representing spectral energy and momentum densities-are evolved and where higher-order moments (e.g., components of the radiation pressure tensor) are approximated using algebraic expressions involving the lower-order, evolved moments to form a closed system of equations.…”

Fully Implicit Time Integration: Fast Solvers and Implicit-Explicit Schemes [Slides]

“…As we discuss in the Section 3, each implicit RK stage solves (15) for I (k) with fixed T . Î includes any forcing terms (in particular, artificial forcing arising from previous stage values).…”

“…Similar asymptotic preserving analysis for the BGK equations is performed in [14]. In [15], an IMEX scheme for relativistic neutrino transport in an astrophysics context is developed. There, the explicit advection time scale for radiation is not problematic, as that is the dynamical timescale of interest, but the local collision physics is stiffer and is treated using a local implicit nonlinear solve.…”

Particle-in-cell Simulation of the Neutrino Fast Flavor Instability

“…To unify and expand on these models, a more general framework for simulating kinetics is needed. Neutrino transport methods such as moment methods [75][76][77][78][79][80][81][82], dis-crete ordinates [83,84], and Monte Carlo [85][86][87][88] could in principle all be extended to treat coherent flavor effects [89,90], but the strong dependence of the evolution of each neutrino on integrals of nearby neutrino distributions is challenging to implement efficiently.…”