Geodesic Mesh MHD: A New Paradigm for Computational Astrophysics and Space Physics Applied to Spherical Systems

Abstract

A majority of astrophysics and space physics systems tend to be spherical. The logically Cartesian r-\(\theta \)-\(\phi \) meshes that are often used in simulations of such systems suffer from a few major deficiencies such as nonuniform coverage of space, loss of accuracy close to the pole, and severe limitation on time stepping. Additionally, it becomes increasingly important to have higher orders of accuracy in order to reduce the dissipation and dispersion. In this work, we describe a new finite volume implementation of MHD equations on a triangular geodesic mesh that is accurate up to fourth order. To achieve the accuracy, we use a combination of: (a) WENO methods, (b) A re-formulation to support higher order divergence-free reconstruction of magnetic field, (c) multidimensional Riemann solvers, (d) higher order timestepping to match the spatial accuracy. A few representative test problems are presented here to highlight the utility of our present approach.