Gyrokinetic simulations of turbulent transport: size scaling and chaotic behaviour

Abstract

Important steps towards the understanding of turbulent transport have been made with the development of the gyrokinetic framework for describing turbulence and with the emergence of numerical codes able to solve the set of gyrokinetic equations. This paper presents some of the main recent advances in gyrokinetic theory and computing of turbulence. Solving 5D gyrokinetic equations requires state-of-the-art high performance computing techniques involving massively parallel computers and parallel scalable algorithms. The various numerical schemes that have been explored until now, Lagrangian, Eulerian and semi-Lagrangian, each have their advantages and drawbacks. A past controversy regarding the finite size effect (finite ρ *) in ITG turbulence has now been resolved. It has triggered an intensive benchmarking effort and careful examination of the convergence properties of the different numerical approaches. Now, both Eulerian and Lagrangian global codes are shown to agree and to converge to the flux-tube result in the ρ * → 0 limit. It is found, however, that an appropriate treatment of geometrical terms is necessary: inconsistent approximations that are sometimes used can lead to important discrepancies. Turbulent processes are characterized by a chaotic behaviour, often accompanied by bursts and avalanches. Performing ensemble averages of statistically independent simulations, starting from different initial conditions, is presented as a way to assess the intrinsic variability of turbulent fluxes and obtain reliable estimates of the standard deviation. Further developments

The global version of the gyrokinetic turbulence code GENE

“…As a side effect, judgments on the validity of local simulations for specific devices can be drawn. Naturally, the details of such a study depend to some extent on the chosen radial profiles which has been shown elsewhere [46,15,47]. In the present case, peaked temperature and density gradient profiles are chosen of the form…”

Interaction between neoclassical effects and ion temperature gradient turbulence in gradient- and flux-driven gyrokinetic simulations

“…The general trend that turbulent transport decreases with growing ρ * is a well established observation. 14,[19][20][21][22] Due to the narrow profile shape (see above) the convergence to the local limit occurs at relatively small ρ * . At this point it is important to remember that the fluxes are measured in units which imply the gyro-Bohm scaling, i.e.…”

Parallel filtering in global gyrokinetic simulations

“…This is a difficult task as bursts are chaotic: the turbulence has a so-called intrinsic variability. This phenomenon has been studied in [26] and [38] for ORB5 simulations: identical simulations differing only by the initialization are performed, and are compared by applying a moving time-average of width ∆t w . A standard deviation over the ensemble of simulations of about 15% is found for ∆t w = 500a/c s .…”