Hermite-Laguerre Spectral Velocity Formulation of Gyrokinetics

Noah Mandell, Princeton University

First-principles simulations of tokamak turbulence have proven to be of great value in recent decades. We develop a spectral velocity formulation of the turbulence equations that smoothly interpolates between the highly efficient but lower-resolution three-dimensional gyrofluid representation and the conventional but more expensive five-dimensional gyrokinetic representation. Our formulation is a projection of the nonlinear gyrokinetic equation onto a Hermite-Laguerre velocity space basis. This model is appropriate for the study of instabilities, turbulence and transport in a wide range of geometries, including tokamaks and stellarators.

We present a new code, GRYFX++, which solves the 5-D gyrokinetic equation in our new Hermite-Laguerre spectral velocity basis. GRYFX++ is an upgrade of the existing 3-D gyrofluid turbulence code GRYFX. Both codes use CUDA to run on NVIDIA GPUs. In addition to generalizing GRYFX to arbitrary velocity space resolution, the CUDA implementations in GRYFX++ have been optimized, making GRYFX++ three to four times faster than GRYFX.

Abstract Author(s): Noah Mandell, Bill Dorland