Geodesic
Quasimonotonous 2D MHD scheme for unstructured meshes
Matematičeskoe modelirovanie, Tome 17 (2005) no. 12, pp. 87-109

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The generalized Lax–Friedrichs scheme is designed for the ideal MHD system. The governing system representing a 2,5D flow model is considered for plane geometry. The second-order difference approximations are done to the MHD equations written in the form of conservation laws. The set of control volumes is conjoined with basic triangular mesh and is generated starting from some initial partition which is usually the Voronoi diagram of basic triangulation. The procedure of time–advance is an explicit predictor-corrector which provides the second order approximation to MHD system in time. The constructed algo-rithms are examined in numerical experiments with known MHD problems related to flows resulted from break of MHD discontinuities and the test results are presented. 
@article{MM_2005_17_12_a3,
     author = {V. A. Gasilov and S. V. D'yachenko},
     title = {Quasimonotonous {2D} {MHD} scheme for unstructured meshes},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {87--109},
     publisher = {mathdoc},
     volume = {17},
     number = {12},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2005_17_12_a3/}
}
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V. A. Gasilov; S. V. D'yachenko. Quasimonotonous 2D MHD scheme for unstructured meshes. Matematičeskoe modelirovanie, Tome 17 (2005) no. 12, pp. 87-109. http://geodesic.mathdoc.fr/item/MM_2005_17_12_a3/