Computer simulation using particles
Computer simulation using particles
Partially linearized algorithms in gyrokinetic particle simulation
Journal of Computational Physics
Gyrokinetic simulation of finite-beta plasmas on parallel architecture
Gyrokinetic simulation of finite-beta plasmas on parallel architecture
Finite Element Methods with B-Splines
Finite Element Methods with B-Splines
Journal of Computational Physics
A drift-kinetic semi-Lagrangian 4D code for ion turbulence simulation
Journal of Computational Physics
Hi-index | 31.45 |
In the last decade, it became clear that electromagnetic (gyro)kinetic particle-in-cell (PIC) simulations are very demanding in respect to numerical methods and the number of markers used. The Monte Carlo discretization of the gyrokinetic equations leads to a severe signal-to-noise problem: the statistical representation of the physically irrelevant but numerically dominant adiabatic current causing a high statistical noise level. The corresponding inaccuracy problem is very pronounced at high plasma @b and/or small perpendicular wave numbers k"@?. We derive several numerical schemes to overcome the problem using an adjustable control variates method which adapts to the dominant adiabatic part of the gyro-center distribution function. We have found that the inaccuracy problem is also present in the quasi-neutrality equation as a consequence of the p"@?-formulation [T.S. Hahm, W.W. Lee, A. Brizard, Nonlinear gyrokinetic theory for finite-beta plasmas, Phys. Fluids 31 (1988) 1940]. For slab simulations in the magnetohydrodynamic (MHD) limit k"@?-0, the number of markers can be reduced by more than four orders of magnitude compared to a conventional @df scheme. The derived schemes represent first steps on a road to fully adaptive control variates method which can significantly reduce the inherent statistical noise of PIC codes.