Invariant conservative finite-difference schemes for the one-dimensional shallow water magnetohydrodynamics equations in Lagrangian coordinates
E. I. Kaptsov, V. A. Dorodnitsyn
备注：
22 pages, 6 figures. This version (v7) has been specially prepared for publication in the Open Commun. Nonlinear Math. Phys., Special Issue in Memory of Professor Decio Levi. Notice that in the previous version (v5) of the paper an appendix was added with an informal discussion on stability issues. By the decision of the authors, this appendix was not included in v6 and v7
发表信息：
Open Communications in Nonlinear Mathematical Physics, Special Issue in Memory of Decio Levi (February 15, 2024) ocnmp:11245
Invariant finite-difference schemes for the one-dimensional shallow water equations in the presence of a magnetic field for various bottom topographies are constructed. Based on the results of the group classification recently carried out by the authors, finite-difference analogues of the conservation laws of the original differential model are obtained. Some typical problems are considered numerically, for which a comparison is made between the cases of a magnetic field presence and when it is absent (the standard shallow water model). The invariance of difference schemes in Lagrangian coordinates and the energy preservation on the obtained numerical solutions are also discussed.
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Laboratoire Jacques-Louis Lions & Centre National de la Recherche Scientifique, Université de Paris 6（雅克-路易·利翁斯实验室与法国国家科学研究中心，巴黎第六大学）；Department of Mathematics, International University（国际大学数学系）
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Laboratoire de Mathématiques de Versailles, UVSQ, CNRS, Université Paris-Saclay（凡尔赛数学实验室，凡尔赛大学，法国国家科学研究中心，巴黎萨克雷大学）；Maison de la Simulation USR 3441, Digiteo Labs, bât. 565, PC 190, CEA Saclay（模拟之家 USR 3441，Digiteo 实验室，CEA 萨克雷）；CEA/DEN/DANS/DM2S/STMF - CEA Saclay（CEA/DEN/DANS/DM2S/STMF - CEA 萨克雷）
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