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.

COCONUT, a Novel Fast-converging MHD Model for Solar Corona Simulations: I. Benchmarking and Optimization of Polytropic Solutions

“…Solar wind models use a wide variety of BCs depending on the physical properties that they want to conserve the most (Zanni & Ferreira 2013;Yeates et al 2018). In Brchnelova et al (2022a), we have experimented with many of them for the COCONUT model, and have come to the conclusion that the most important aspect was to minimize the currents at the surface of the star, which is achieved through the BCs described below.…”

“…We must however point out that, due to numerical precision, the boundary outflow is never exactly 0, which means that our BC is actually equivalent to setting a minimal outflow at the surface of the star. We have also tested aligning the velocity with the magnetic field to limit the generation of currents close to the star, but in the end, we selected this BC due to the fact that it helps the streamers be better collimated (Brchnelova et al 2022a). We will show more about that in Section 3.…”

“…While these simulations generally had worse convergence, they proved that the final results were mostly mesh-topology-independent and thus that the differences observed between the COCONUT and Wind-Predict solutions were due to other numerical aspects. For more details about the impact of the mesh on the solution, see Brchnelova et al (2022b).…”

COCONUT, a novel fast-converging MHD model for solar corona simulations: II. Assessing the impact of the input magnetic map on space-weather forecasting at minimum of activity

“…The inner velocity is set to 0 at the inner boundary by following the prescription: V x,y,zG = −V x,y,zI . This condition allows us to suppress the currents at the solar surface in order to produce a better perfect conductor boundary condition (see Perri et al (2022) and Brchnelova et al (2022a) for more details).…”

COCONUT, a novel fast-converging MHD model for solar corona simulations: I. Benchmarking and optimization of polytropic solutions

“…While these simulations generally had worse convergence, they proved that the final results were mostly mesh-topology-independent and thus that the differences observed between the CF and Wind-Predict solutions were due to other numerical aspects. For more details about the impact of the mesh on the solution, see Brchnelova et al (2022b).…”