Event Type:

Applied Mathematics and Computation Seminar

Date/Time:

Friday, May 21, 2021 - 12:25 to 12:50

Location:

ZOOM

Event Link:

Guest Speaker:

Sebastian Naranjo

Abstract:

We apply the framework of the Virtual Element Method (VEM) to a model in Magneto-HydroDynamics (MHD), that incorporates a coupling between electromagnetics and fluid flow, to construct novel discretizations for simulating realistic phenomenon in MHD. First, we study two chains of spaces approximating the electromagnetic and fluid flow components of the model. Then, we show that this VEM approximation will yield divergence free discrete magnetic fields that is an important property in any simulation in MHD. We present a linearization strategy to solve the VEM approximation which respects the divergence free condition on the magnetic field. This linearization will require that, at each non-linear iteration, a linear system be solved. We study these linear systems and show that they represent well-posed saddle point problems. We conclude by presenting numerical experiments exploring the performance of the VEM applied to the subsystem describing the electromagnetics, and in particular the magnetic reconnection problem.