Abstract

An approach for describing the metric properties of a difference mesh for discretizing repeated rotational operations of vector analysis as applied to modeling electromagnetic fields is proposed. Based on the support operator method, integral-consistent operations (gradient, divergence and curl) are constructed, which are necessary to obtain estimates of the convergence of difference schemes for repeated rotational operations designed to solve specific problems of magnetohydrodynamics. Using smooth solutions of a model magnetostatic problem with first-order accuracy, the convergence of the difference schemes constructed in this work with a zero eigenvalue of the spectral problem is proved. In this case, no restrictions are imposed on the difference tetrahedral mesh, except for its nondegeneracy. Calculation of electromagnetic fields for a three-dimensional problem of magnetic hydrodynamics in a two-temperature approximation with the full set of spatial components of velocity and electromagnetic fields is presented. The dynamics of electromagnetic fields is developed against the background of rotational diffusion of the magnetic field vector.

中文翻译：

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重复旋转运算支持算子方法的一些差分格式的收敛性

摘要

提出了一种描述差分网格的度量属性的方法，用于离散化应用于电磁场建模的矢量分析的重复旋转操作。基于支持算子方法，构造了积分一致运算（梯度、散度和旋度），这对于获得旨在解决磁流体动力学特定问题的重复旋转运算的差分格式的收敛性估计是必需的。使用具有一阶精度的模型静磁问题的平滑解，证明了本文构造的差分格式在谱问题的零特征值下的收敛性。在这种情况下，除了其非简并性之外，对差分四面体网格不施加任何限制。提出了在具有速度和电磁场的全套空间分量的二温度近似下的磁流体动力学三维问题的电磁场计算。电磁场动力学是在磁场矢量旋转扩散的背景下发展起来的。