As the largest gravitationally bound objects in the universe, galaxy clusters are a unique probe of large scale cosmological structure. Determining the distribution of galaxy clusters and their virial masses may be key to constraining properties of dark energy and dark matter. Since 84%of a typical galaxy cluster's mass is comprised of non-radiating dark matter, however, determining the virial mass of galaxy clusters depends on inference from the radiating baryonic matter. 84%of this baryonic matter is contained in the intracluster medium (ICM)-a hot, diffuse, magnetized plasma permeating the galaxy cluster. While the baryonic matter is the only emitter of observable electromagnetic emissions from galaxy clusters, the complex behavior of the ICM as a turbulent magnetized plasma makes constraining the virial mass of the cluster with observable signatures difficult. Numerical simulations are essential tools for advancing understanding of the ICM and for tying galaxy cluster observables to virial masses. The goal of this dissertation is to explore and enable simulations of galaxy clusters and magnetized plasmas via a number of different avenues.I first explore self-regulation of feedback from active galactic nuclei (AGN) preventing over-cooling in cool-core (CC) clusters-galaxy clusters with anomalously high central thermal emission which should cool on shorter timescales than they persist. In the idealized galaxy cluster simulations with a thermal abstraction of AGN feedback, we find that the thermal-only heating kernels we test are unable to offset cooling while maintaining a realistic structure, suggesting exploration of more complex AGN feedback mechanisms such as those including magnetic fields and turbulence.We then explore how kinetic and magnetic energy thermalizes in the ICM by studying decaying magnetized turbulence with simulations of the magnetized compressible Taylor-Green vortex. Using a shell-to-shell energy transfer analysis, we find that the magnetic fields facilitate a significant amount of the energy flux that is not seen in hydrodynamic turbulence. Although the full cascade will not be directly captured in ICM simulations for the foreseeable future, higher resolution simulations enabled by larger computational resources can diminish such effects.Different novel many-core architectures have emerged in recent years on the way toward larger supercomputers in the exascale era. Performance portability is required to prevent repeated nontrivial refactoring of a code for different architectures. To address the need for a performance portable magnetohydrodynamics (MHD) code, we combined Athena++, an existing MHD CPU code, with Kokkos, a performance portable framework, into K-Athena to allow efficient simulations on multiple architectures using a single codebase. K-Athena has also inspired the Parthenon performance portable adaptive mesh refinement (AMR) framework. Using this framework, we developed the performance portable AMR MHD code AthenaPK.Galaxy clusters contain significant magnetic fields, although their origin and role is still under investigation. Numerical modeling is essential for the inference of their properties. One aspect is whether magnetic AGN feedback models can self-regulate. I present work-in-progress simulations with AthenaPK of magnetized galaxy clusters slated for exascale supercomputers later this year.With the higher resolutions enabled by exascale systems, galaxy cluster simulations with relativistic jet velocities will be possible. Robust methods for relativistic plasmas will be needed. With this goal, I present a discontinuous-Galerkin (DG) method for relativistic hydrodynamics. We include an exploration of different methods to recover the primitive variables from conserved variables, a new operator for enforcing a physically permissible conserved state, and numerous tests of the method. This method has been used at Sandia National Laboratories to study terrestrial plasmas and will inform relativistic MHD methods for AthenaPK.Finally, I cover the future directions of the work in this dissertation, including the many codes enabled by Parthenon, additions to the magnetized galaxy cluster simulations with AthenaPK, and the large body of projects at Los Alamos National Laboratory to explore binary black hole mergers embedded within AGN accretion disks as a possible formation channel of the massive black holes observed by LIGO. The work in this dissertation to develop performance portable plasma simulations will enable ground-breaking simulations for years to come.
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