The Predictor–Corrector Method for Solving of Magnetohydrodynamic Problems

In the present work for solution of magnetohydrodynamic problems, the finite difference method of predictor–corrector type is chosen as basic. This method allows fulfilling above requirements on the algorithm constructing. At a predictor step, the initial equations are approximated in nondivergent form and the special splitting scheme on physical processes and spatial variables is proposed. The splitting of operators at fractional steps includes two steps: the splitting on spatial directions as in most schemes of approximate factorization and the special splitting of each one-dimensional problem so that the scheme is unconditionally stable but realized by scalar sweeps at the fractional steps on the one hand and on the other hand has minimal quantity of additional members arising from splitting. Proposed special splitting form of one-dimensional operators allows to minimize the splitting effect that makes these schemes to be similar to nonfactorizing schemes. At a corrector step, the equations are approximated on divergent form to satisfy the scheme conservative property. For linearized equations, it can be shown that proposed scheme is unconditionally stable in two-dimensional case. Efficiency of proposed algorithm is shown on solving the problem about high-temperature plasma spread in the magnetic field. Influence of the magnetic field on plasma configuration, and change of plasma shape in time are studied and plasma spread speed is evaluated.