Dynamic procedure for filtered gyrokinetic simulations

Abstract

Large Eddy Simulations (LES) of gyrokinetic plasma turbulence are investigated as interesting candidates to decrease the computational cost. A dynamic procedure is implemented in the GENE code, allowing for dynamic optimization of the free parameters of the LES models (setting the amplitudes of dissipative terms). Employing such LES methods, one recovers the free energy and heat flux spectra obtained from highly resolved Direct Numerical Simulations (DNS). Systematic comparisons are performed for different values of the temperature gradient and magnetic shear, parameters which are of prime importance in Ion Temperature Gradient (ITG) driven turbulence. Moreover, the degree of anisotropy of the problem, that can vary with parameters, can be adapted dynamically by the method that shows Gyrokinetic Large Eddy Simulation (GyroLES) to be a serious candidate to reduce numerical cost of gyrokinetic solvers. I. MOTIVATION AND CONTEXTIn the area of fluid turbulence, theories are usually based on the notion of an inertial range in which the energy cascades from larger scales to (somewhat) smaller scales mediated by the quadratic nonlinearity. The role of the smallest scales is then to dissipate energy in the so-called dissipative range. In numerical simulations, this picture has led to the development of Large Eddy Simulation (LES) techniques that are based on the idea that neglecting the small scales can be compensated by introducing a dissipative model for the eddy viscosity 1 .A Direct Numerical Simulation (DNS) is supposed to retain all the scales from the injection range down to the dissipative range. This requires an enormous numerical effort in the case of high Reynolds number flows. On the contrary, a LES coarsens the simulation grid and only retains the largest scales (which are problem-dependent), while the small scales (which are assumed to be universal) are replaced by a model. In Fourier space, such a coarsening can be seen as the action of a low-pass filter. Since the scale range is truncated, the dissipation scales can not be reached, and the modeling basically consists of the introduction of artificial dissipation mechanisms. From a more mathematical viewpoint, one notes that the filtering operation does not commute with the nonlinear term that transfers energy from largest to smallest scales, and the major problem of LES consists in finding a satisfying closure for representing the influence of the unresolved scales.Recent gyrokinetic studies have shown that Ion Temperature Gradient (ITG) driven turbulence exhibits a direct and local cascade of a nonlinear invariant, namely the free energy. 2 Such a cascade is analogous to the kinetic energy cascade in three dimensional NavierStokes turbulence. The important difference is that the a) pmorel@ulb.ac.be quadratic conserved quantity in fluid dynamics is the kinetic energy, while it is the free energy in gyrokinetics. The latter quantity is the sum of both the perturbed entropy and the electrostatic energy. Transfers between entropy and electrostatic energy ar...

Phase mixing versus nonlinear advection in drift-kinetic plasma turbulence

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Applications of large eddy simulation methods to gyrokinetic turbulence

“…In addition, the dissipative effect on the model is guaranteed by setting to zero any negative coefficient value 20 .…”

“…Since all the information of free energy transfer T k is a available in addition to the largest scale one, we can also calculate T < k|kc as the difference of the two. This method was used in previous works 19,20 to study the properties of the sub-grid transfer. It was found out that its effect is to systematically dissipate free energy from the system.…”

“…Hence, the LES technique used for simulation fluid turbulence has been applied to plasma turbulence, first using simpler shearing-rate based subgrid models in gyrofluid 16 and gyrokinetic 17 simulations, and recently using more advanced dynamic sub-grid models 19,20 . The same ideas, to resolve the largest scales in the system and model the influence of small ones, are applied to the gyrokinetic equations and give rise to the Gyrokinetic Large Eddy Simulation (GyroLES) approach.…”

The Hamiltonian Structure and Euler-Poincare Formulation of the Valsov-Maxwell and Gyrokinetic System

“…It is not yet clear if it is possible to design a regularization of this type for the gyrokinetic system that retains the redundancy of the U fields and allows one to write down a standard Vlasov equation. We note that gyrokinetic LES has been explored and implemented recently on the GENE code, by adding hyperdiffusive terms in the perpendicular co-ordinates 36,58 .…”