Gyrokinetic Dynamic Fidelity Refinement

Gyrokinetic Dynamic Fidelity Refinement is described and demonstrated. The basic problems are familiar from AMR techniques, but there are differences. Our proposed method is pseudo-spectral in all five dimensions $(x, y, z, v_\parallel, \mu B)$. Mesh refinement occurs by changing the number of Fourier, Hermite, or Laguerre basis functions, according to a dynamic target refinement metric. Low amplitude turbulence (near marginal stability) requires relatively high resolution in Hermite-Laguerre space, but modest resolution in $k$-space. High amplitude turbulence (away from marginal stability) requires relatively low resolution in Hermite-Laguerre space, but higher resolution in $k$. Stochastic echoes limit the $v$-space resolution requirements at high amplitude. Nonlinear phase-mixing ultimately limits the required $k_\perp$ resolution, as it provides a physical hyperviscosity mechanism. Depending on the quality of the closures available at low $v$-space resolution, GKDFR should be the optimal algorithm for evaluating small $\rho_*$, electromagnetic, gyrokinetic turbulence within the TRINITY multiscale transport framework.