Convergence of Some Iterative Algorithms for the Numerical Solution of Two-Dimensional Nonstationary Problems of Magnetic Hydrodynamics

This paper studies the convergence of methods of a combined and separate solution of difference equations groups, splitted by physical processes, applied to a family of completely conservative difference schemes (CCDSs) of two-dimensional magnetohydrodynamics (MHD). Estimates are obtained for the convergence of iterative processes for the entire family of CCDSs, both for the method of a separate and combined solution of groups of difference equations. These results are obtained for the first time; previously, such estimates were obtained only for a purely implicit difference scheme. The validity of the estimates obtained in this study is confirmed by the numerical calculations. Based on the estimates obtained in this study, recommendations are developed for any CCDS, whose numerical method is more appropriate to use to solve the system of difference equations. Depending on the ratio of the parameters of the substance and the electromagnetic field at each moment of time, the estimates obtained in this study, even for calculating one physical problem of two-dimensional MHD, make it possible to choose the optimal numerical method for each time integration step, which leads to a significant reduction in the computational time of the problem. This can be quite important, especially when conducting a large-scale computational experiment. Thus, the results obtained in this study have not only an interesting theoretical but also an important practical value.