Development of a gyrokinetic hyperbolic solver based on discontinuous Galerkin method in tokamak geometry

Nonlinear Fokker-Planck collision operator in Rosenbluth form for gyrokinetic simulations using discontinuous Galerkin method

“…In applying DG methods, there have been growing interests for gyrokinetic whole device modeling of tokamak [33,35]. DG methods provide many advantages in the gyrokinetic WDM of tokamak plasma.…”

“…In this work, a nonlinear collision operator based on the Fokker-Planck RMJ form is formulated in gyrokinetic variables and numerically implemented in the DG-based gyrokinetic code [35]. In addition to the nonlinear collision operator, linear and Dougherty collision models are implemented as well to assess the benefits and drawbacks of each model.…”

“…The computing time for each collision operator is summarized in Table 3. Currently, the code [35] in which collision operators of this work are implemented is based on the C++ language and supplemented by Intel MKL libraries. While the code is MPI-parallelized for multi-core simulations, a single CPU is used for this benchmark, since each spatial cell is assigned to a single CPU core and the velocity space is not MPI-parallelized.…”

“…Although these equations are not suitable for the quantitative micro-turbulence study, they are sufficient to investigate neoclassical physics in the drift kinetic limit. More details about the implementation of these equation for DG simulations are given in [35]. The third-order SSP3 Runge-Kutta method [41] is used for the time integration of gyrokinetic equations, as well as the collision operator.…”