A preconditioned semi-implicit method for magnetohydrodynamics equations

The paper describes the development of a semi-implicit solver designed for the need to follow slow evolution flows encountered in nonlinear resistive computational plasma dynamics (CPD). Spatial discretization uses a second order finite difference approximation while temporal advance is achieved by a second order semi-implicit predictor-corrector scheme that reduces the severe time step constraints imposed by the fast magnetosonic and Alfven waves on standard explicit schemes. An efficient preconditioner adapted to magnetohydrodynamics (MHD) problems and associated with conjugate gradient-like linear solvers considerably increases the CPU saving when compared with an explicit advance. This scheme enables the use of a large time step as well as the necessary high spatial resolution. An application of this scheme to a class of astrophysical nonlinear MHD problems allows one to perform numerical experiments relevant to the slow MHD evolution of the magnetic field, dominating the outer atmosphere of the sun, that leads to small scales formation.