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

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dc.creatorGardiner, Thomas A.
dc.creatorStone, James M.
dc.date2007-12-17
dc.date.accessioned2026-07-07T11:13:47Z
dc.date.available2026-07-07T11:13:47Z
dc.descriptionWe 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.
dc.descriptionExtended version of the paper accepted for publication in JCP
dc.identifierhttps://arxiv.org/abs/0712.2634
dc.identifierhttp://arxiv.org/abs/0712.2634
dc.identifierJ.Comput.Phys.227:4123-4141,2008
dc.identifierdoi:10.1016/j.jcp.2007.12.017
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/191843
dc.subjectAstrophysics
dc.titleAn Unsplit Godunov Method for Ideal MHD via Constrained Transport in Three Dimensions
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