A semi-Lagrangian code for nonlinear global simulations of electrostatic drift-kinetic ITG modes

Abstract

A semi-Lagrangian code for the solution of the electrostatic drift-kinetic equations in straight cylinder configuration is presented. The code, CYGNE, is part of a project with the long term aim of studying microturbulence in fusion devices. The code has been constructed in such a way as to preserve a good control of the constants of motion, possessed by the drift-kinetic equations, until the nonlinear saturation of the ion-temperature-gradient modes occurs. Studies of convergence with phase space resolution and time-step are presented and discussed. The code is benchmarked against electrostatic Particle-in-Cell codes.

A drift-kinetic Semi-Lagrangian 4D code for ion turbulence simulation

“…A less dissipative solution which simply consists in replacing the cubic spline interpolation of the distribution function by the cubic spline interpolation of the logarithm of this distribution function is developed and compared to the PFC method in [28] for the 2D standard Landau damping case. However it requires an increase of the mesh refinement to treat correctly the small scales [42]. Given that a simulation with a mesh of (128 · 256 · 128 · 64) needs more than 7 GBytes of memory and 25 s of CPU time for each iteration on 128 processors, more refined meshes are difficult to use given the present resources.…”

“…Besides, benchmarks with two PIC codes (the linear code LORB5 [9] and the non-linear code ORB5 [8]) reveal good agreement (cf. [42]). …”

Development of a Grid-Based Gyro-Kinetic Simulation Code

“…A detailed description of the numerical scheme can be found in [1]. In summary, the code is based on the semi-Lagrangian approach, the 4D distribution function f is represented on a fixed grid in phase space.…”

“…Its simulation in the frame of the 5 dimensional gyrokinetic equations represents a challenging numerical problem. As a first step toward the treatment of the 5D system in toroidal geometry, a 4D code, CYGNE [1], is being developed for solving the electrostatic drift-kinetic equations in cylindrical geometry. This code uses a semi-Lagrangian approach based on cubic spline interpolation.…”

Quasisteady and steady states in global gyrokinetic particle-in-cell simulations

“…The main difficulties come from the Courant-Friedrich-Levy ͑CFL͒ condition and the convergence with respect to the grid size, which can be difficult to show. The semi-Lagrangian method [21][22][23][24] uses a fixed grid in time whereas the gyrokinetic equation is integrated along trajectories. This method removes the CFL condition but, as for Eulerian simulations, can lead to negative values of the distribution function.…”