Semi-implicit anisotropic cosmic ray transport on an unstructured moving mesh

TL;DR

This paper introduces a new semi-implicit anisotropic cosmic ray transport solver on an unstructured moving mesh, improving accuracy, efficiency, and robustness for simulating cosmic ray effects in galaxy and cluster evolution.

Contribution

The paper presents a novel anisotropic diffusion solver that is conservative, entropy-preserving, and supports semi-implicit integration with local timesteps on unstructured moving meshes.

Findings

Solver performs as well or better than previous methods.

Reproduces global timestep results with local timesteps at lower computational cost.

Effective in complex galaxy formation simulations.

Abstract

In the interstellar medium of galaxies and the intracluster gas of galaxy clusters, the charged particles making up cosmic rays are moving almost exclusively along (but not across) magnetic field lines. The resulting anisotropic transport of cosmic rays in the form of diffusion or streaming not only affects the gas dynamics but also rearranges the magnetic fields themselves. The coupled dynamics of magnetic fields and cosmic rays can thus impact the formation and evolution of galaxies and the thermal evolution of galaxy clusters in critical ways. Numerically studying these effects requires solvers for anisotropic diffusion that are accurate, efficient, and robust, requirements that have proven difficult to satisfy in practice. Here, we present an anisotropic diffusion solver on an unstructured moving mesh that is conservative, does not violate the entropy condition, allows for semi-implicit time integration with individual timesteps, and only requires solving a single linear system of equations per timestep. We apply our new scheme to a large number of test problems and show that it works as well or better than previous implementations. Finally, we demonstrate for a numerically demanding simulation of the formation of an isolated disk galaxy that our local time-stepping scheme reproduces the results obtained with global time-stepping at a fraction of the computational cost.