When constructing difference schemes for calculating complex problems of computational astrophysics considering magnetohydrodynamic and gravitational phenomena, the processes of matter overcompression (with a change in density by several orders of magnitude) should be taken into account, and it is important at a discrete level to take into account the corresponding energy transformations of magnetohydrodynamic, gravitational, kinetic, and internal energy during the evolution of a star. This problem is solved by constructing completely conservative difference schemes in a view of these magnetohydrodynamic processes and self‐gravitating phenomena. In this work, to study and apply the difference methods for solving problems of magnetic gas dynamics, a discrete representation of symmetrized spatial deformations of the medium was obtained. The representation is consistent with changes in the magnetic, kinetic, and internal energies and does not lead to their distortions when the matter is overcompressed.

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关于计算天体物理问题中磁流体动力学现象的一些积分一致方法

在构造考虑磁流体动力学和引力现象的计算天体物理学复杂问题的差异方案时，应考虑物质过压缩的过程（密度变化几个数量级），在离散水平上考虑这一点很重要考虑到恒星演化过程中相应的磁流体动力，引力，动能和内能的能量转换。鉴于这些磁流体动力学过程和自重现象，通过构造完全保守的差分方案可以解决该问题。在这项工作中，为了研究和应用不同的方法来解决磁性气体动力学问题，获得了介质对称空间变形的离散表示。