Ideal MHD and constrained transport for finite volume and finite element schemes
The ideal MHD equations are used in many applications in plasma physics and astrophysics. I will show why it is of primary importance to develop stable schemes that preserve the divergence-free nature of the magnetic field, in order to avoid spurious dynamo effects. Godunov methods have been developed in the finite volume framework to deliver such stable schemes. Higher order methods have also been designed recently for the ideal MHD equations. I will present our recent work on the Spectral Difference method for ideal MHD which preserve the divergence free property of the solution both in a local and a global sense, and compares favourably with the widely used Discontinuous Galerkin method.
Romain Teyssier is Professor of Computational Astrophysics at the University of Zürich, where he teaches physics, astrophysics, and computational science. He is an expert in cosmology, galaxy formation, and star formation. He is the main author of the RAMSES code, a massively parallel Adaptive Mesh Refinement code for self-gravitating, magnetized, radiative flows. Teyssier's main research activity is to perform simulations of cosmic structure using supercomputers, in order to understand the origin of astrophysical objects such as stars (like our Sun) and galaxies (like our Milky Way). He is also modelling the evolution of the entire Universe in the context of the Euclid mission.