Astronomy and Astrophysics – Astrophysics
Scientific paper
2005-01-25
J.Comput.Phys. 205 (2005) 509-539
Astronomy and Astrophysics
Astrophysics
45 pages, 13 figures, accepted for publication in J. Comp. Phys., More information on Athena can be found at http://www.astr
Scientific paper
10.1016/j.jcp.2004.11.016
We describe a single step, second-order accurate Godunov scheme for ideal MHD based on combining the piecewise parabolic method (PPM) for performing spatial reconstruction, the corner transport upwind (CTU) method of Colella for multidimensional integration, and the constrained transport (CT) algorithm for preserving the divergence-free constraint on the magnetic field. We adopt the most compact form of CT, which requires the field be represented by area-averages at cell faces. We demonstrate that the fluxes of the area-averaged field used by CT can be made consistent with the fluxes of the volume-averaged field returned by a Riemann solver if they obey certain simple relationships. We use these relationships to derive new algorithms for constructing the CT fluxes at grid cell corners which reduce exactly to the equivalent one-dimensional solver for plane-parallel, grid-aligned flow. We show that the PPM reconstruction algorithm must include multidimensional terms for MHD, and we describe a number of important extensions that must be made to CTU in order for it to be used for MHD with CT. We present the results of a variety of test problems to demonstrate the method is accurate and robust.
Gardiner Thomas A.
Stone James M.
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