A CONSISTENT METHOD OF CHARACTERISTICS FOR MULTIDIMENSIONAL MAGNETOHYDRODYNAMICS

This paper introduces a previously unaddressed problem with performing multidimensional numerical MHD characterized by ''explosive'' growth (within a single time step) of weak magnetic fields to possibly dynami c strengths in the vicinity of strong velocity shear. This problem has been observed to occur in numerical algorithms which rely on the solu tion of the characteristic equations at the mesh interfaces. The solut ion to this problem is the subject of this paper and has led to an alg orithm fundamentally different from those discussed previously. Specif ically, at every point on the mesh, the magnetic induction terms are d etermined from the characteristic velocities which are evaluated by so lving implicitly (in space) the characteristic equations for incompres sible MHD (although the algorithm is perfectly suitable for compressib le MHD). The implicit treatment of the characteristic equations sets t his algorithm apart from previous efforts and is shown to be a necessa ry condition for multidimensional accuracy. It amounts to replacing th e usual directional-split treatment of the induction and transport ope rators with a planar-split scheme.