Piecewise parabolic method on local stencil. IV. Multidimensional ideal MHD

Technique for solving of ideal MHD equations on the basis of piecewise parabolic method on local stencil (PPML) is suggested. PPML uses the property of Riemann invariants to conserve when moving along the characteristic curves of MHD equations, what allows to use local stencil for constructing numerical solution. This approach improves the dissipative properties of the numerical scheme and must be convenient in adaptive grids. Basic elements of the scheme constructing technique are illustrated for 2D case. A question about maintaining of nondivergence constraint on magnetic field is considered. Testing of the scheme was carried out with the help of some typical 2D test problems.