The application of fully conservative difference schemes to the calculation of two-dimensional magnetohydrodynamic systems

Abstract

A fully conservative difference schemes (FCDS) for calculating two-dimensional non-stationary MHD currents described in Eulerian variables is constructed. The conductivity of the medium is assumed to be ideal. The specific form of the difference schemes is implemented on a rectilinear lattice in Cartesian coordinates with two different orientations of the magnetic field induction vector. The general form of the description of the schemes we construct admits of the use of curvilinear lattices. The schemes considered enable us to calculate the currents for large and small values of the ratio of the matter pressure to the magnetic field. The quality of fully-conservative difference schemes and conservative difference schemes is compared using the example of the numerical solution of a model problem.