Foundations Of Computational Mathematics (FoCM 2005)

Workshop on Foundations of Numerical PDEs

July 7 - July 9, 2005

Universidad de Cantabria in Santander, Spain

MHD Equations, the div(B) Constraint, and Central Schemes

Jorge Balbas

Department of Mathematics at University of Michigan

Abstract:   Simulations of Magnetohydrodynamical (MHD) flows pose computational challenges that extend beyond the development of discontinuous solutions typical of non-linear hyperbolic systems. In particular, an additional constraint on the magnetic field, div(B) = 0, needs to be satisfied to guarantee the stability of the numerical schemes. We will discuss some of these challenges, the techniques commonly employed to overcome them, and the capability of central schemes to handle them in a rather simple manner. To this end, we present computational results that indicate a remarkable ability of certain "black box" type central schemes to address these difficulties.