Numerical Methods for Plasma Astrophysics:
From Particle Kinetics to MHD

CSIC Building (#406), Seminar Room 4122.
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Combining Godunov Schemes with Constrained Transport for MHD

Dr. Thomas Gardiner

Astrophysical Sciences at Princeton University

Abstract:   The system of equations for MHD differs from its hydrodynamic counterpart by the presence of a multidimensional constraint; the magnetic field must be divergence free. If this constraint fails to be satisfied, the primitive and conservative form of the equations for MHD are inconsistent leading to numerical instabilities. These instabilities are particularly destructive to Godunov schemes which integrate the system of equations in conservative form. Godunov schemes are based upon the idea of physically realizing the initially discrete solution in a continuous space. The Constrained Transport (CT) method is a simple, intuitive approach to discretizing the magnetic field components such that it can always be realized in a continuous space and be consistent with the div B=0 condition. I will describe the challenges to combining CT with Godunov schemes and their resolution in the Athena simulation code.