A full-implicit-continuous-Eulerian (FICE) scheme for multidimensional transient magnetohydrodynamic (MHD) flows

A full implicit continuous Eulerian (FICE) scheme is developed for solving multidimensional transient MHD flow problems. The physical system under consideration is a general case of a transient MHD flow in which an initial steady state is subject to a finite amplitude disturbance. The governing equations are described, their finite difference formulation is presented and the FICE algorithm is given. The boundary conditions are treated by classifying them into physical and computational ones. The usefulness of the FICE algorithm is demonstrated using a physical example concerning the dynamical response of the static solar atmosphere due to a representative photospheric disturbance.