Recent Upgrades in a 2D Turbulent Transport Solver Based on a Hybrid Discontinuous Galerkin Method for the Simulation of Fusion Plasma in Tokamak

Abstract

The simulation of fusion plasmas in realistic magnetic configurations and tokamak geometries still requires the development of advanced numerical algorithms owing to the complexity of the problem. In this context, we propose a Hybrid Discontinuous Galerkin (HDG) method to solve 2D transport fluid equations in realistic magnetic and tokamak wall geometries. This high-order solver can handle magnetic equilibrium free structured and unstructured meshes allowing a much more accurate discretization of the plasma facing components than current solvers based on magnetic field aligned methods associated with finite-differences (volumes) discretization. In addition, the method allows for handling realistic magnetic equilibrium, eventually non steady, a critical point in the modeling of full discharges including ramp up and ramp down phases. In this paper, we introduce the HDG algorithm with a special focus on recent developments related to the treatment of the cross-field diffusive terms, and to an adaptive mesh refinement technique improving the numerical efficiency and robustness of the scheme. The updated solver is verified with a manufactured solution method, and numerical tests are provided to illustrate the new capabilities of the code.

Keywords

• Hybrid Discontinuous Galerkin
• fusion plasma modeling
• tokamak
• adaptive refinement