Of mesh artefacts and electric fields: the bane of numerical global coronal modelling

Global magnetohydrodynamic (MHD) computational fluid dynamics (CFD) simulations have become an important tool for solar weather research. These simulations use solar magnetogram data to compute structures in the solar corona. We have developed one such model based on the COOLFLuiD platform and validated it through comparison with other state-of-art codes and observations (Leitner et al., 2022, submitted). Currently, further physics is added to the solver to move it from ideal MHD to full MHD, such as radiation, coronal heating or conduction. Description of this physics and its results is what is most usually discussed in papers concerning coronal MHD CFD. 

However, physics is only one part of the solution when CFD is used. Actually, it is the numerics that is oftentimes the limiting factor, setting constraints on the accuracy and speed of these solvers. Many different problems can arise due to the finite discretisation of the domain or even due to the solver working with simplified ideal MHD equations instead of the full ones. It is rarely discussed what type of a computational grid should be used depending on the type of the simulations at hand, and it is mentioned even less often what type of errors and inaccuracies such an inappropriate grid type can cause. An unsuitable grid can also cause convergence problems and decrease the speed of the solver considerably (Brchnelova et al., 2022, submitted).

In our work, we investigate the sources of inaccuracies and errors which can compromise the global coronal MHD CFD results. We have observed that due to the large ranges of density magnitudes involved, spurious numerical fluxes can result on mesh cell interfaces when these cells are either highly skewed or the boundaries otherwise non-orthogonal. These spurious fluxes can create local errors of up to 40% in the velocity field in the most deformed portions of the computational grid. Further inaccuracies were observed also in the sharpness of the resulting velocity structures, this time due to artificially generated electric fields during the simulation. 

Thus, in our talk, we will summarize the most important of the issues observed, their causes and potential means of their mitigation. For controlling the errors due to the spurious fluxes while simultaneously optimizing the performance of the solver, we will show a trade-off between different grid topologies and what to expect in the results. Similarly, to enhance the sharpness of the features, it will also be discussed how to mitigate the generation of artificial electric fields via careful formulation of the initial state and boundary conditions.

This research has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 870405 (EUHFORIA 2.0) and the ESA project "Heliospheric modelling techniques“ (Contract No. 4000133080/20/NL/CRS).