Speaker
Description
Nonlinear hyperbolic balance laws with stiff source terms arise in many multiphysics problems, including astrophysical flows where hydrodynamics is coupled with chemical processes. In this work we consider a system of hyperbolic balance laws describing a shock–cloud interaction with a simplified chemical network for ionisation and recombination. This framework is useful in studying the large-scale propagation of astrophysical jets in active galactic nuclei (AGN) through the inhomogeneous ambient medium of their host galaxies, see \cite{A}. Standard explicit time-integration methods are severely restricted by stability constraints in the presence of stiffness, often requiring prohibitively small time steps.
Minimally Implicit Runge–Kutta (MIRK) schemes provide an efficient alternative time-integration strategy by introducing only a minimal level of implicitness while retaining favourable stability properties. These methods have already shown promising results in other applications involving hyperbolic balance laws as the resistive relativistic magnetohydrodynamic equations\cite{B}, the neutrino transport equations\cite{C} and the 1D shallow water equations\cite{D}. Here we investigate their performance for the present system and compare them with standard explicit Runge–Kutta methods in terms of stability, accuracy, and computational efficiency through a series of numerical experiments.
\bibitem{A}
Perucho, M., López‐Miralles, J., Reynaldi, V., & Labiano, Á. (2021). Jet propagation through inhomogeneous media and shock ionization. Astronomische Nachrichten, 342(9-10), 1171-1175.
\bibitem{B}
Cordero-Carrión, I., Santos-Pérez, S., Martı́nez-Vidallach, C., Numerical evolution of the resistive
relativistic magnetohydrodynamic equations: A minimally implicit Runge-Kutta scheme, Applied
Mathematics and Computation, 443, 127774, 2023.
\bibitem{C}
Santos-Pérez, S., Obergaulinger, M., Cordero-Carrión, I.. Minimally implicit methods for the
numerical integration of the neutrino transport equations, arXiv preprint arXiv:2302.12089, 2023.
\bibitem{D}
Martı́nez-Donato, I., Cabllero-Cárdenas, C., Gómez-Bueno, I., Cordero-Carrión, I., A fast and
minimally implicit fully well-balanced scheme for the 1D shallow water system with topography
and Manning friction, Submitted to Mathematical Modelling and Numerical Analysis.