We present an assessment of the accuracy of a recently developed MHD code used to study hydromagnetic flows in supernovae and related events. The code, based on the constrained transport formulation, incorporates unprecedented ultra-high-order methods (up to 9th order) for the reconstruction and the most accurate approximate Riemann solvers. We estimate the numerical resistivity of these schemes in tearing instability simulations.

The instability due to a vertical uniform temperature gradient is studied in a rapidly rotating horizontal layer of an electrically conducting fluid permeated by an azimuthal magnetic field linearly growing with the distance from the vertical axis of rotation. In addition to the boundary conditions used in So ward's study (1979), that is, force-free surface and perfect electrical and thermal conductivity outside, also other conditions more realistic for the Earth's core are considered, that is, rigid surface and electrically insulating walls. Using the concept of meanfield mlid mean electromotive and ponderomotive forces (E.M.F. and P.M.F.) are calculated and compared for various boundary conditions. The dependence of the E.M.F. and P.M.F. on the electromagnetic boundary conditions is strong (slight) if the boundaries are free (rigid).