Convergence of Some Difference Schemes of the Support Operator Method for Repeated Rotational Operations

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.