Seminar Announcement
Timothy BarthNASA Ames Research Center"Stable MHD Discretizations"
Date: Monday, October 10, 2005
Abstract:The development of robust simulation software is usually guided by a solid understanding of stability, accuracy, and convergence of the underlying numerical methods. Compressible MHD simulation is certainly no exception. In this work, energy stable MHD discretizations are examined using modified forms of the discontinuous Galerkin method [1]. In this setting, recent numerical analysis [2] offers up several possible discretization schemes that meet the overall software design goal of higher order accuracy and provable energy stability. Unfortunately, some of these energy stable discretizations are considerably more difficult to implement than others so a comparison of the various discretization methods is useful. In this seminar, we briefly recount the relevant MHD numerical analysis results and shift our attention to the design and implementation of robust MHD simulation software using modified forms of the space-time discontinuous Galerkin method. The current solver for both hydrodynamics and MHD permits adjustable order accuracy in both space and time on arbitrary cell complexes composed of triangles and quadrilaterals in 2-D as well as tetrahedra, bricks, prisms, and pyramids in 3-D. Using this solver, comparisons between various MHD discretizations are shown to assess the implementation complexity, algorithmic robustness, and numerical accuracy of these modified discretizations. Finally, the space-time discontinuous Galerkin formulation easily accommodates the construction of a-posteriori error estimates in both space and time. Some research directions taken in this area will then be outlined. [1] W.H. Reed and T.R. Hill, "Triangular Mesh Methods for the Neutron Transport Equation", LANL Report LA-UR-73-479, 1973. [2] T.J. Barth, "On the Role of Involutions in the Discontinuous Galerkin Discretization of Maxwell and Magnetohydrodynamic Systems", IMA Volume on Compatible Spatial Discretizations, Springer-Verlag, NY, Vol. 142, 2005. Also http://science.nas.nasa.gov/~barth/IMA/IMA-2005.pdf
Email: barth@nas.nasa.gov Speaker's web page: http://people.nas.nasa.gov/~barth/
Institution web page: http://www.nasa.gov/centers/ames/home/index.html 
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