Conservative Finite Element Approach to Magnetized Plasma Simulation

The physics of 2D drift-reduced MHD models, including generalizations of the Hasegawa-Mima and Hasegawa-Wakatani models are explored using a new finite element approach to magnetized plasma simulation and compared to results of the GDB finite difference code. These models are implemented using MFEM, a highly scalable finite element library, that can address the challenging physical, geometric, and numerical issues associated with edge plasmas. Recently, we derived and implemented [1] arbitrary polynomial-order finite element spatial discretizations for the drift-reduced magnetohydrodynamics (MHD) equations that conserve both energy and enstrophy to machine precision when coupled with generally symplectic time-integration methods. However, we discovered that the fully conservative model is not accurate at long times and that dissipation must be reintroduced to control the short wavelength part of the spectrum. We found that using an upwinded DG formulation, which dissipates enstrophy while conserving energy, is the most efficient method for generating accurate results for a suite of 2D turbulence test problems. We are extending these results to 3D incompressible MHD and plasma turbulence.

[1] M. Holec, B. Zhu, I. Joseph, et al, arXiv:2202.13022, submitted to J. Comp. Phys. (2022)