Finite Element Simulation of Magnetized Edge Plasma Turbulence

We explore the use of the MFEM framework, a highly scalable finite element library, for addressing the challenging physical, geometric, and numerical issues associated with high-performance simulation of fusion edge plasmas. Adaptive mesh refinement, mesh optimization, high-order discretization, and high-order curved meshes can reduce numerical discretization error by orders of magnitude for cases of interest that correspond to divertors, magnetic islands, and external walls. Several reduced MHD models have been developed that describe magnetized plasma dynamics in 2D: the Navier-Stokes, Hasegawa-Mima, and Hasegawa-Wakatani models. We have developed both linear and nonlinear solvers for the plasma fluid equations, including preconditioning strategies and block preconditioning strategies that address the combination of the ExB flow and anisotropic diffusion.  In addition, an antisymmetric form of the advection operator conserves both energy and enstrophy for arbitrary polynomial order elements, like the Arakawa bracket. The numerical models have been validated by comparing the linear growth rates with predictions of a semi-analytical eigensolver for various conditions and benchmarked with Global Drift Ballooning (GDB) finite difference code.