ABSTRACT:   This talk will present an approximate Riemann solver for nonrelativistic and semirelativistic magnetohydrodynamics. One example of the importance of modeling magnetohydrodynamics is the increasing need to understand and predict the interaction of solar wind with Earth.  In order to provide forecasting in the future and understanding of the physical processes in the present, one needs to have accurate and fast numerical methods to model magnetohydrodynamics (MHD).

A physically real MHD simulation requires that density and pressure remain positive under all circumstances and that no magnetic monopoles are introduced.  It is important to avoid generating magnets with only one pole (monopoles) from a numerical method since monopoles have never been found in nature. The equations describing the fluid may be written as a system of partial differential equations with piecewise constant initial conditions. In mathematics, this situation is called a Riemann problem. Developing numerical solver for MHD that uses a Riemann solver is ideal because the Riemann problem design mathematically ensures the conservation of the physical quantities.

This talk will present a method based on the multi-state HLLC (Harten-Lax-van Leer-Contact) approximate nonlinear Riemann solver for gas dynamics for the ideal magnetohydrodynamics equations written in conservation form. The HLLC solver is based on the assumption that the normal velocity is constant over the Riemann fan and the full seven wave nonlinear Riemann fan may be approximated with three waves. This approximation is intended to resolve slow, Alfv\'{e}n, and contact waves better than the original HLL solver. This solver is a positively conservative variant of Linde's HLLC solver for MHD. Compared to exact nonlinear solvers and Roe's solver, this method is computationally inexpensive. Simulation results will concentrate on one-dimensional test cases for the entire family of two intermediate  state HLL solvers.

This talk will also include a brief description of related problems that are being tackled by a team of three undergraduates at George Washington University.

This talk will assume no knowledge of physics or computational science. Students are encouraged to attend.