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Center for Applied Mathematics (CAM)
Colloquium
Monday, April 16, 2007 at 4:00 p.m.
"RKDG and ADER-DG Schemes with Limiters for Euler and Magnetohydrodynamic Flows"
Dinshaw Balsara
Department of Physics
University of Notre Dame
Room
127 Hayes-Healy
*TEA - 3:30 p.m. in Math Lounge*
Abstract:
Discontinous Galerkin schemes have several features that make them attractive for computing Euler and Magnetohydrodynamic (MHD) flows. They offer high accuracy, a complete representation of the solution and can be adapted for mesh refinement. Yet they also have some limitations that have impeded their practical use. In this talk we address those limitations and provide ways to get past the limitations.
We show first that one can design accuracy preserving limiters for these methods, making it possible to use them for shock-capturing applications. We also show that the methods can be combined with ADER timestepping to offer temporal accuracy that is as high as the spatial accuracy. Traditional DG methods have a rather large memory footprint and we also display methods for reducing the memory footprint in massively parallel applications. The ADER timestepping has also been extended to larger systems such as the MHD system and we also present results on that topic. The topic of divergence-free reconstruction of vector fields in MHD will also be discussed.