Piecewise Parabolic Method on a Local Stencil for Ideal Magnetohydrodynamics

摘要

A numerical scheme based on the piecewise parabolic method on a local stencil (PPML) isproposed for solving the ideal magnetohydrodynamic (MHD) equations. The method makes use of theconservation of Riemann invariants along the characteristics of the MHD equations. As a result, a localstencil can be used to construct a numerical solution. This approach improves the dissipative propertiesof the numerical scheme and is convenient in the case of adaptive grids. The basic stages in the designof the scheme are illustrated in the two-dimensional case. The conservation of the solenoidal propertyof the magnetic field is discussed. The scheme is tested using several typical MHD problems.