Energy conservation and numerical stability for the reduced MHD models of the non-linear JOREK code
For researchers using the JOREK code for non-linear MHD simulations, this work improves physical accuracy and numerical stability.
This work derives a more complete reduced MHD model for the JOREK code that includes terms necessary for exact energy conservation, and replaces the linearized time stepping with a non-linear Inexact Newton method with adaptive time stepping, which improves robustness and allows larger time steps in the non-linear phase.
In this paper we present a rigorous derivation of the reduced MHD models with and without parallel velocity that are implemented in the non-linear MHD code JOREK. The model we obtain contains some terms that have been neglected in the implementation but might be relevant in the non-linear phase. These are necessary to guarantee exact conservation with respect to the full MHD energy. For the second part of this work, we have replaced the linearized time stepping of JOREK by a non-linear solver based on the Inexact Newton method including adaptive time stepping. We demonstrate that this approach is more robust especially with respect to numerical errors in the saturation phase of an instability and allows to use larger time steps in the non-linear phase.