## Project A4

# Projectleader

Prof. Dr. Christiane Helzel

Institute for Numerical Mathematics

Ruhr-University Bochum

# Title

Logically rectangular grid methods for the simulation of compressible MHD

equations in circular and spherical domains

# Summary

The ideal magnetohydrodynamic (MHD) equations are important in modeling phenomena in a

wide range of applications, including solar physics, laboratory plasmas and astrophysical fluid

flow. Here we are concerned with the construction of numerical methods for these equations.

They have to master the challenge of producing approximations that remain accurate near shock

waves and that satisfy a divergence free constraint of the magnetic field.

This project focuses on the development of numerical methods for the MHD equations in cir-

cular and spherical domains which are of interest in solar physics, e.g. for the simulation of

coronal mass ejection (CME). We are constructing mapped grid methods which are based on

mappings of a single Cartesian grid to the sphere or other spherical domains. These mappings

have recently been introduced in the context of finite volume methods for hyperbolic problems

and are now being applied to the MHD equations.