A h-Adaptivity Strategy for Hybridizable Discontinuous Galerkin (HDG) Simulations of Fluid Transport Models in Tokamak Plasma

Abstract

The highly anisotropic, multi-scale nature of fusion plasma simulations in tokamaks, combined with the complexity in the geometries of plasma-facing components and magnetic equilibrium, challenges numerical schemes. They therefore require the development of advanced numerical techniques to enhance computational efficiency and enable codes to simulate realistic plasma configurations relevant to tokamak operation. This paper proposes an adaptive mesh refinement strategy ($h$-adaptivity) in the SolEdge-HDG code for the resolution of 2D fluid-drift Braginskii equations using the Hybrid Discontinuous Galerkin (HDG) method. The strategy is based on an oscillation indicator implemented to detect under-resolved regions and dynamically refine the mesh, associated with an a posteriori accuracy indicator built on the local difference between the solution at order $p$ and the post-processed one at order $p+1$ considered as reference. The method thus enables both refinement, where necessary, as well as coarsening in regions where the solution is smooth. Numerical results obtained with this method in realistic tokamak geometry and plasma conditions show significant reductions in computational resources and an improvement in code robustness while maintaining high accuracy, particularly in regions with steep gradients or near the sharp angles of the tokamak walls. This work highlights the potential of such $h$-adaptivity technique to optimize transport simulations in realistic tokamak configurations, offering a fully automated, goal-oriented mesh refinement strategy. In addition to optimizing the numerical cost of simulation, this strategy offers all users a fully automated means of designing a mesh in any tokamak geometry.