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.

翻译：在各种底部地形的存在下，构建了一维浅水方程在磁场存在情况下的有限差分方案。基于作者最近进行的群分类结果，得到了原微分模型的守恒定律的有限差分模拟。数值上考虑了一些典型问题，比较了磁场存在和不存在（标准浅水模型）的情况。还讨论了在拉格朗日坐标系中的差分方案的不变性以及获得的数值解上的能量守恒。