The technique of solution of the magnetohydrodynamics tasks in quasi-Lagrangian variables

A method of numerical solution of one-dimensional magnetohydrodynamics (MHD) problems taking into account volume losses and sources of mass is presented. The governing MHD system of equations is written in quasi-Lagrangian variables defined by the initial distribution of the substance. A family of implicit completely conservative difference schemes is constructed. The developed technique has been approved by the numerical experiments with the tasks for which self-similar analytical solutions exist. The computational 1D model based on the quasi-Lagrangian approach may be useful as a means of non-consuming computations with partial taking into account of the effects caused by two- or three-dimensional motion of the substance.