Numerical study of the plasma tearing instability on the resistive time scale

In this work, a new numerical scheme for the reduced resistive MHD system (RMHD) is presented. Numerical simulations of RMHD are notoriously challenging because of the disparate time-scales, encompassing the Alfvén wave period and the resistive diffusion time, and because of the formation of thin internal layers, especially in the nonlinear phase. The new scheme is specifically designed for the study of the long time scale dynamics with large time steps. The key difficulty, namely the singularity of the system matrix in the limit of an infinite time scale disparity, is overcome by techniques inspired by asymptotic preserving (AP) methods. The reformulated version of the fully-implicit RMHD scheme is based on a 'micro-macro' (MM) scheme with a stabilization term. The tearing mode evolution and the formation of a magnetic island are considered as a test case. The advantages of the MM scheme with respect to standard implicit and explicit schemes are demonstrated. Good agreement with known analytical results in the regime of nonlinear growth and saturation of the magnetic island are obtained.