Astronomy and Astrophysics – Astrophysics
Scientific paper
2007-12-17
J.Comput.Phys.227:4123-4141,2008
Astronomy and Astrophysics
Astrophysics
Extended version of the paper accepted for publication in JCP
Scientific paper
10.1016/j.jcp.2007.12.017
We present a single step, second-order accurate Godunov scheme for ideal MHD which is an extension of the method described by Gardiner & Stone (2005) to three dimensions. This algorithm combines 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 describe the calculation of the PPM interface states for 3D ideal MHD which must include multidimensional ``MHD source terms'' and naturally respect the balance implicit in these terms by the ${\bf\nabla\cdot B}=0$ condition. We compare two different forms for the CTU integration algorithm which require either 6- or 12-solutions of the Riemann problem per cell per time-step, and present a detailed description of the 6-solve algorithm. Finally, we present solutions for test problems to demonstrate the accuracy and robustness of the algorithm.
Gardiner Thomas A.
Stone James M.
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