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Center for Nonlinear Studies |
Godunov type integration algorithms have ideal dissipation characteristics for simulating moderate to high Mach number hydrodynamic systems. Unfortunately, the extension of these methods to handle ideal magnetohydrodynamics (MHD) has been traditionally hampered by stability issues related to the magnetic charge constraint, div B = 0. Adopting the method of Constrained Transport (CT) ameliorates these stability issues, but raises additional stability concerns resulting from the CT electric field algorithm which relates the Godunov fluxes to the CT electric fields. In this talk I will review the approximations (and exact relationships) which underlie the development of finite volume, Godunov-type algorithms for MHD using CT and in particular present the essential elements which went into developing the MHD algorithms in the Athena simulation code. These include the development of a new set of CT electric field algorithms, the extension of the PPM interface state algorithm for multidimensional MHD, and the incorporation of these algorithms into the unsplit corner transport upwind (CTU) integration algorithm. Along the way, I will present a variety of test problems to help clarify the discussion and highlight the characteristics of the integration algorithms. As time permits, I will close the talk with a discussion of current algorithm development efforts including adaptive mesh refinement and non-ideal extensions.
Host: Mikhail Shashkov