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.
Highlights
In order to show the new capability of the code to run with different cross-field coefficients, Equations (1)–(4) are resolved in the WEST geometry (Figure 1)
Lowering D makes the parallel transport dominant that can be very demanding for the solver, in the present configuration where the mesh is not aligned along the magnetic field lines [8]
This paper presents a high-order solver based on the Hybrid Discontinuous Galerkin method to perform plasma simulations in tokamak
Summary
We have recently considered a Hybrid Discontinuous Galerkin (HDG) method Such discretization based on structured or unstructured meshes is magnetic equilibrium free that allows for accurate simulations of the whole vacuum chamber whatever the geometrical complexity of the tokamak wall or the magnetic equilibrium shape. It allows for handling a non-steady magnetic equilibrium [6]—a critical point to model a full discharge including start-up and shut-down phases [7]. We present an updated algorithm for solving 2D fluid–drift
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