Numerical Simulation of Magnetic Field Effects on Symmetrically Collapsing Fluids

The work presented here is part of a project with the aim to develop a tool allowing to model a symmetrical collapse of a fluid in the presence of magnetic fields. To that end, we use a Python-based numerical solver and implemented both the fluid dynamics part and electromagnetics. In this contribution, we focus on the coupling between both parts and in particular on solving the magnetoquasistatic Maxwell equations in the employed Lagrangian framework. A preliminary study has shown that the latter copes best with the complexity of the system. Moreover, throughout the project, we have tested several methods to reduce numerical errors. Their efficiency is illustrated. The resulting solver is then applied to study selected setups: at first, we present results of a successful benchmark of the pure Navier-Stokes part against reference data available in the literature. Encouraged by the outcome of the benchmark, we then tackle some coupled problems comprising cases which can be analytically solved. Finally, we discuss properties of our solver and indicate potential future tasks.