A multistep implicit scheme for time-dependent 2-dimensional magnetohydrodynamic flows

It is well known that many solar phenomena take place in or near active regions where the magnetic fields are so strong as to play a predominant role in supporting, heating, and accelerating the plasma. The time step would be severely restricted by the CFL condition and a long time computation would be subjected to numerical instability if an explicit method were adopted in these cases. In addition, improper treatment of the artificial boundaries one has to introduce in order to limit the size of the computational domain often leads to unphysical reflections. An implicit algorithm for solving time-dependent, 2-dimensional magnetohydrodynamic equations is presented which consists of a multistep implicit scheme for discretizing the governing equations and the projected characteristic method for stipulating artificial boundary conditions. The algorithm is illustrated by a physical problem concerning the dynamical response of the static atmosphere to a magnetic flux emergence of opposite polarity from below the photosphere. The stability criteria are given for both the scheme and the projected characteristic method.