Numerical Methods for Plasma Astrophysics:
From Particle Kinetics to MHD

CSIC Building (#406), Seminar Room 4122.
Directions: home.cscamm.umd.edu/directions

High Resolution Methods for Constrained Transport in MHD

Dr. Eitan Tadmor

Center for Scientific Computation and Mathematical Modeling (CSCAMM)
Institute for Physical Science & Technology (IPST), and
Department of Mathematics
University of Maryland, College Park

Abstract:   A trademark of nonlinear, time-dependent, convection-dominated problems is the spontaneous formation of non-smooth macro-scale features, like shock discontinuities and non-differentiable kinks, which pose a challenge for high-resolution computations. We overview recent developments of modern computational methods for the approximate solution of such problems. In these computations, one seeks piecewise smooth solutions which are realized by finite dimensional projections. Computational methods in this context can be classified into two main categories, of local and global methods. Local methods are expressed in terms of point-values (-- Hamilton-Jacobi equations), cell averages (-- nonlinear conservation laws), or higher localized moments.

High resolution central schemes will be discussed as a prototype example for local methods. The family of central schemes offers high-resolution ``black-box-solvers'' to an impressive range of such nonlinear problems with or without constrained transport. The main ingredients here are detection of spurious extreme values, non-oscillatory reconstruction in the directions of smoothness, numerical dissipation and quadrature rules.