Development of a Hybrid Simulation Code with Grid-based Continuum Kinetics

In weakly collisional or collisionless astrophysical systems, large-scale plasma dynamics are entwined with magnetic field structure, while transport phenomena are governed by small-scale kinetic particle interactions. Numerical simulations of such systems are therefore a natural application of hybrid fluid-kinetic models that capture physics across these scales while maintaining reasonable computational cost. Hybrid models typically utilize particle-in-cell (PIC) methods for the kinetic ions, but PIC methods suffer from noise and are best suited for phenomena with high signal-to-noise ratios. One alternative is to use a grid-based kinetic model, which evolves the noise-free, continuous distribution function. While grid-based methods are known to be computationally expensive due to the large number of degrees of freedom, advances in numerical techniques have made such methods more feasible. In this work, we present the design of a hybrid code combining the finite volume (FV) magnetohydrodynamics (MHD) capabilities of the FLASH code with the discontinuous Galerkin (DG) Vlasov solver of the GKEYLL simulation framework. Average plasma quantities are described by the single-fluid MHD equations with an extension for separate electron, ion, and radiation temperatures. To incorporate kinetic ion behavior, ions are evolved with the Vlasov equation in the frame moving with the bulk plasma fluid velocity, and ion pressure and heat flux moments are computed for use in the MHD equations. Ion quantities exist on a coarser grid than the MHD fluid to allow for simple interpolation between FV and DG representations.