@article{6344efba23454c5b96332ed9758d367b,
title = "Global high-order numerical schemes for the time evolution of the general relativistic radiation magneto-hydrodynamics equations",
abstract = "Modeling correctly the transport of neutrinos is crucial in some astrophysical scenarios such as core-collapse supernovae and binary neutron star mergers. In this paper, we focus on the truncated-moment formalism, considering only the first two moments (M1 scheme) within the grey approximation, which reduces Boltzmann seven-dimensional equation to a system of 3 + 1 equations closely resembling the hydrodynamic ones. Solving the M1 scheme is still mathematically challenging, since it is necessary to model the radiation-matter interaction in regimes where the evolution equations become stiff and behave as an advection-diffusion problem. Here, we present different global, high-order time integration schemes based on Implicit-Explicit Runge-Kutta methods designed to overcome the time-step restriction caused by such behavior while allowing us to use the explicit Runge-Kutta commonly employed for the magneto-hydrodynamics and Einstein equations. Finally, we analyze their performance in several numerical tests.",
keywords = "methods: numerical, neutrinos, radiative transfer, relativistic processes, software: simulations, stars: neutron",
author = "Izquierdo, {M. R.} and L. Pareschi and B. Mi{\~n}ano and J. Mass{\'o} and C. Palenzuela",
note = "Funding Information: We are indebted with David Radice for many useful discussions on the neutrino transport problem. We also thank Martin Obergaulinger for many clarifications on the subject. Finally, it is a pleasure to thank Miguel Bezares for reviewing an earlier version of the manuscript. C P acknowledges the hospitality at the Institute for Pure & Applied Mathematics (IPAM) through the Long Program {\textquoteleft}Mathematical and Computational Challenges in the Era of Gravitational Wave Astronomy{\textquoteright}, where this Project was initiated. M R I thanks financial support PRE2020-094166 by MCIN/AEI/PID2019-110301GB-I00 and by {\textquoteleft}FSE invierte en tu futuro{\textquoteright}. L P would like to thank the Italian Ministry of Instruction, University and Research (MIUR) to support this research with funds coming from PRIN Project 2017 (No. 2017KKJP4X entitled {\textquoteleft}Innovative numerical methods for evolutionary partial differential equations and applications{\textquoteright}). This work was supported by the Grant PID2019-110301GB-I00 funded by MCIN/AEI/10.13039/501100011033 and by {\textquoteleft}ERDF A way of making Europe{\textquoteright} (J M and C P). Publisher Copyright: {\textcopyright} 2023 IOP Publishing Ltd.",
year = "2023",
month = jul,
day = "20",
doi = "10.1088/1361-6382/acd97f",
language = "English",
volume = "40",
journal = "Classical and Quantum Gravity",
issn = "0264-9381",
publisher = "IOP Publishing ",
number = "14",
}