thornado-hydro: a discontinuous Galerkin method for supernova hydrodynamics with nuclear equations of state

TL;DR

This paper develops and tests a high-order discontinuous Galerkin method within the thornado toolkit for simulating supernova hydrodynamics, incorporating nuclear equations of state and advanced limiters to improve accuracy and robustness.

Contribution

It introduces extended limiters for RKDG methods to handle nuclear EoS and demonstrates their effectiveness in supernova-related hydrodynamics simulations.

Findings

Extended limiters improve method robustness.

Bound-enforcing limiter enhances stability in collapse simulations.

Slope limiting faces challenges with phase transitions in EoS.

Abstract

This paper describes algorithms for non-relativistic hydrodynamics in the toolkit for high-order neutrino radiation hydrodynamics (thornado), which is being developed for multiphysics simulations of core-collapse supernovae (CCSNe) and related problems with Runge-Kutta discontinuous Galerkin (RKDG) methods. More specifically, thornado employs a spectral type nodal collocation approximation, and we have extended limiters - a slope limiter to prevent non-physical oscillations and a bound-enforcing limiter to prevent non-physical states - from the standard RKDG framework to be able to accommodate a tabulated nuclear equation of state (EoS). To demonstrate the efficacy of the algorithms with a nuclear EoS, we first present numerical results from basic test problems in idealized settings in one and two spatial dimensions, employing Cartesian, spherical-polar, and cylindrical coordinates. Then, we apply the RKDG method to the problem of adiabatic collapse, shock formation, and shock propagation in spherical symmetry, initiated with a 15 solar mass progenitor. We find that the extended limiters improve the fidelity and robustness of the RKDG method in idealized settings. The bound-enforcing limiter improves robustness of the RKDG method in the adiabatic collapse application, while we find that slope limiting in characteristic fields is vulnerable to structures in the EoS - more specifically, in the phase transition from nuclei and nucleons to bulk nuclear matter. The success of these applications marks an important step toward applying RKDG methods to more realistic CCSN simulations with thornado in the future.