Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 227, Issue 8, Pages 4123-4141Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2007.12.017
Keywords
magnetohydrodynamics; numerical methods; compressible flow
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We present a single step, second-order accurate Godunov scheme for ideal MHD which is an extension of the method described in [T.A. Gardiner, J.M. Stone, An unsplit godunov method for ideal MHD via constrained transport, J. Comput. Phys. 205 (2005) 509] 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 del.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. (C) 2007 Elsevier Inc. All rights reserved.
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