Advanced Energy and Enstrophy Conserving FEM for Drift-Reduced MHD

In this work, we explore a high-order time and space discretization for edge plasma turbulence simulations. A drift-reduced extended magnetohydrodynamics model describes turbulence driven by the Kelvin-Helmholtz and drift wave instabilities coupled to the shear Alfven wave. The theory of finite element spaces and collocation integration schemes provides a high-order space and time discretization that satisfies physical constraints including energy and enstrophy conservation and ensuring divergence-free magnetic and drift velocity fields up to machine precision. In particular, we show how a specific choice of time and space discretization tackles the conservation while eliminating numerical artifacts such as dissipation of energy and enstrophy. Moreover, the schemes do not only conserve integrated quantities, but also show noticeable effects on the spatial distribution of the flow itself. The performance and advantages of our proposed discretization are demonstrated using simulations of plasma flows, such as decaying and forced Hasegawa-Mima turbulence.