XTOR-2F: A fully implicit Newton–Krylov solver applied to nonlinear 3D extended MHD in tokamaks

XTOR-2F solves a set of extended magnetohydrodynamic (MHD) equations in toroidal tokamak geometry. In the original XTOR code, the time stepping is handled by a semi-implicit method [1], [2] and [3]. Moderate changes were necessary to transform it into a fully implicit one using the NITSOL library with Newton–Krylov methods of solution for nonlinear system of equations [4]. After addressing the sensitive issue of preconditioning and time step tuning, the performances of the semi-implicit and the implicit methods are compared for the nonlinear simulation of an internal kink mode test case within the framework of resistive MHD including anisotropic thermal transport. A convergence study comparing the semi-implicit and the implicit schemes is presented. Our main conclusion is that on one hand the Newton–Krylov implicit method, when applied to basic one fluid MHD is more computationally costly than the semi-implicit one by a factor 3 for a given numerical accuracy. But on the other hand, the implicit method allows to address challenging issues beyond MHD. By testing the Newton–Krylov method with diamagnetic modifications on the dynamics of the internal kink, some numerical issues, to be addressed further, are emphasized.