Using the Hybridizable Discontinuous Galerkin Method for Simulating far-SOL fluid transport within the MAPS (MFEM Anisotropic Plasma Solver) Code

Radio frequency (RF) heating plays an important role in current and upcoming tokamaks. However, experiments show there are adverse effects such as RF sheath rectification, density depletion through ExB convective cells, and loss of heating efficiency in the far-SOL associated with RF wave edge-plasma interactions. Numerically simulating the coupled interaction of RF waves with transport provides a more comprehensive method of understanding the underlying behavior of these non-linear effects to optimize RF heating scenarios. This work focuses on the transport component of the integrated modeling efforts. Here, the status of the finite-element equilibrium fluid transport code, MAPS (MFEM [1] Anisotropic Plasma Solver), will be reported on. A new code based on the recent hybridizable discontinuous Galerkin (HDG) finite-element method [2] now allows for the solving of complex advection-diffusion fluid problems which have been problematic for the DG method MAPS currently relies on. We will report the development efforts of implementing this HDG formulation in the MFEM library to be used within the MAPS code for further optimization.

[1] https://mfem.org/

[2] N.C. Nguyen et. al, “An implicit high-order hybridizable discontinuous Galerkin method for linear convection–diffusion equations,” Journal of Computational Physics 228 (2009) 3232–3254