# Time integration for neutrino radiation transport using minimally implicit Runge-Kutta methods

## TL;DR

This paper introduces a new minimally implicit Runge-Kutta method for stable, efficient neutrino-radiation hydrodynamics simulations, suitable for stiff equations in astrophysics.

## Contribution

The paper presents a novel minimally implicit Runge-Kutta approach that allows analytical inversion, reducing computational cost while handling stiffness in neutrino-matter interaction equations.

## Key findings

- Method effectively handles stiff neutrino-matter reactions.
- Application to supernova simulations demonstrates stability and efficiency.
- Results show accurate modeling of neutrino transport in astrophysical environments.

## Abstract

The evolution of many astrophysical systems is dominated by the interaction between matter and radiation such as photons or neutrinos. The dynamics can be described by the evolution equations of radiation hydrodynamics in which reactions between matter particles and radiation quanta couples the hydrodynamic equations to those of radiative transfer (see Munier & Weaver (1986a) and Munier & Weaver (1986b)). The numerical treatment has to account for their potential stiffness (e.g., in optically thick environments). In this article, we will present a new method to numerically integrate these equations in a stable way by using minimally implicit Runge-Kutta methods. With these methods, the inversion of the implicit operator can be done analytically, so the computational cost is equivalent to that of an explicit method. We strongly take into account the physical behavior of the evolved variables in the limit of the stiff regime in the derivation of the methods. We will show the results of applying these methods to the reactions between neutrinos and matter in some tests and also in realistic core-collapse supernovae simulations.