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In this paper we present a rigorous derivation of the reduced MHD models withand without parallel velocity that are implemented in the non-linear MHD codeJOREK. The model we obtain contains some terms that have been neglected in theimplementation but might be relevant in the non-linear phase. These arenecessary to guarantee exact conservation with respect to the full MHD energy.For the second part of this work, we have replaced the linearized time steppingof JOREK by a non-linear solver based on the Inexact Newton method includingadaptive time stepping. We demonstrate that this approach is more robustespecially with respect to numerical errors in the saturation phase of aninstability and allows to use larger time steps in the non-linear phase.

Energy conservation and numerical stability for the reduced MHD models of the non-linear JOREK code