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We assess the validity of a single step Godunov scheme for the solution of the magneto-hydrodynamics equations in more than one dimension.
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A. Dedner, F. Kemm, D. Kröner, C.D. Munz, T. Schnitzer, M. Wesenberg, Hyperbolic divergence cleaning for the MHD equations, J. Comput. Phys. 175 (2002) 645-673
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A. Artebrant, M. Torrilhon, Increasing the accuracy in locally divergence-preserving finite-volume schemes for MHD, J. Comput. Phys. 227 (2008) 3405-3427
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2004
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D.S. Balsara, J. Kim, A comparison between divergence-cleaning and staggered-mesh formulations for numerical magnetohydrodynamics, ApJ 602 (2004) 1079
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P. Londrillo, L. Del Zanna, On the divergence-free condition in GOdunov-type schemes for ideal magnetohydrodynamics: the upwind constrained transport method, J. Comput. Phys. 195 (2004) 17
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U. Ziegler, A central-constrained transport scheme for ideal magnetohydrodynamics, J. Comput. Phys. 196 (2004) 393
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R.K.Crockett, P. Colella, R.T. Fisher, R.I. Klein, C.F. McKee, An Unsplit, cell-centered Godunov method for ideal MHD, J. Comput. Phys. 203 (2005) 422
2005
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T. Gardiner, J. Stone, An unsplit Godunov method for ideal MHD via constrained transport, J. Comput. Phys. 205 (2005) 509
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2008
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J.W. Banks, T. Aslam, W.J. Rider, On sub-linear convergence for linearly degenerate waves in capturing schemes, J. Comput. Phys. 227 (2008) 6985-7002
2008
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T. Gardiner, J. Stone, An unsplit Godunov method for ideal MHD via constrained transport in three dimensions, J. Comput. Phys. 227 (2008) 4123
2008
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S. Massaglia, G. Bodo, A. Mignone, P. Rossi, Jets From Young Stars III: Numerical MHD and Instabilities, Lecture Notes in Physics, Volume 754. ISBN 978-3-540-76966-8. Springer-Verlag Berlin Heidelberg, 2008
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D. Lee, A.E. Deane, An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics, J. Comput. Phys. 228 (2009) 952
2009
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