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

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 and Weaver 1986a Comput. Phys. Rep. 3 127; 1986b Comput. Phys. Rep. 3 165). 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. In deriving the methods, we explicitly account for the behaviour of the evolved variables in the stiff regime. 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.