Application of Hybridizable Discontinuous Galerkin discretization for modelling of plasma transport in tokamaks

Power exhaust, particle and energy spatial distribution are key to the performance of tokamaks. Understanding the relation between these aspects and plasma properties, plasma scenario and plasma-facing components is instrumental in the design of optimized plasmas on the way to energy production through fusion.

The laboratory M2P2 (Aix-Marseille Université, CNRS, Ecole Centrale Méditerranée), along with several collaborating research entities, is involved in the development of numerical tools towards the modelling of particle and energy circulation in the tokamak as well as heat flux on plasma-facing components through the 2D fluid transport code SolEdge-HDG. The latter is a steady-state solver, based on a high-order finite-element spatial discretization named Hybridizable Discontinuous Galerkin, in which the geometry of the wall is fully taken into account by adequate meshes that are constructed regardless of the magnetic field.

The presentation will first bring a short introduction to Discontinuous Galerkin methods for the non-specialists, before moving to Hybridizable Discontinuous Galerkin methods, their working principle, distinctive features and perceived advantages. The presentation will then focus more in-depth on the code Soledge-HDG through a brief overview of the underlying physics, of the equations solved, general algorithm and workflow for a typical simulation. A final part will describe recent works, highlighting the capacity of the code to deal with time-varying magnetic fields and adaptive mesh refinement.