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arXiv · 0712.2634

An Unsplit Godunov Method for Ideal MHD via Constrained Transport in Three Dimensions

Thomas A. Gardiner·James M. Stone
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Abstract

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.

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Thomas A. Gardiner, James M. Stone. 2007-12-17. An Unsplit Godunov Method for Ideal MHD via Constrained Transport in Three Dimensions. https://doi.org/10.1016/j.jcp.2007.12.017

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