Spring 2016
Seminars are held on Mondays from 2:30 - 3:30PM in Cullimore Hall, Room 611, unless noted otherwise. For questions about the seminar schedule, please contact David Shirokoff.
Date: February 15, 2016
Speaker: David Seal
Department of Mathematics,
U.S. Naval Academy
Title: "Finite Difference Methods for Magnetohydrodynamics Equations"
Abstract:
In this work we present novel finite difference weighted ENO (WENO) methods tailored for the magnetohydrodynamic (MHD) equations. These equations define a class of fluid plasma models that have been successful at modeling many physical phenomenon including galaxy formation, simulation of solar wind, and even modeling of liquid metals. The full set of equations look like a coupling of Navier-Stokes to Maxwell's equations. Our focus is on ideal MHD, in which case the system reduces to a hyperbolic conservation law. We make use of unstaggered constrained transport in order to obtain divergence free magnetic fields at the discrete level. This is an important property for any numerical method for this system. In addition, our solver is single-stage and single-step, therefore it is amenable to adaptive mesh refinement (AMR). Space is discretized using classical finite difference WENO methods, and time is discretized through Taylor series. The entire method is viewed as a method of modified fluxes, that allows us retain positivity of the pressure and density is by coupling the entire solver to a flux limiter. Results for several classical problems from the literature are presented, including including Orzag-Tang, cloud shock interactions, and blast wave problems.