Effects of mesh topology on MHD solution features in coronal simulations

Abstract

Magnetohydrodynamic (MHD) simulations of the solar corona have become more popular with the increased availability of computational power. Modern computational plasma codes, relying upon computational fluid dynamics (CFD) methods, allow the coronal features to be resolved using solar surface magnetograms as inputs. These computations are carried out in a full three-dimensional domain and, thus, selection of the correct mesh configuration is essential to save computational resources and enable/speed up convergence. In addition, it has been observed that for MHD simulations close to the hydrostatic equilibrium, spurious numerical artefacts might appear in the solution following the mesh structure, which makes the selection of the grid also a concern for accuracy. The purpose of this paper is to discuss and trade off two main mesh topologies when applied to global solar corona simulations using the unstructured ideal MHD solver from the COOLFluiD platform. The first topology is based on the geodesic polyhedron and the second on $UV$ mapping. Focus is placed on aspects such as mesh adaptability, resolution distribution, resulting spurious numerical fluxes and convergence performance. For this purpose, first a rotating dipole case is investigated, followed by two simulations using real magnetograms from the solar minima (1995) and solar maxima (1999). It is concluded that the most appropriate mesh topology for the simulation depends on several factors, such as the accuracy requirements, the presence of features near the polar regions and/or strong features in the flow field in general. If convergence is of concern and the simulation contains strong dynamics, then grids which are based on the geodesic polyhedron are recommended compared with more conventionally used $UV$ -mapped meshes.