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 [1-3]. 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.