A split control variate scheme for PIC simulations with collisions

JOURNAL OF COMPUTATIONAL PHYSICS

卷:295

Article

Sonnendruecker, Eric^1,3  Wacher, Abigail¹  Hatzky, Roman¹  Kleiber, Ralf² 

[1] Max Planck Inst Plasma Phys, D-85748 Garching, Germany

[2] Max Planck Inst Plasma Phys, D-17491 Greifswald, Germany

[3] Tech Univ Munich, Ctr Math, D-85747 Garching, Germany

关键词: Vlasov-Poisson system;    Fokker-Planck;    Collisions;    Particle in cell;    PIC;    Monte Carlo;    Control variate;   

DOI  :  10.1016/j.jcp.2015.04.004

来源: Elsevier

【 摘 要 】

When the distribution function of plasma particles stays close to some analytically known function, statistical noise inherent to Monte Carlo simulations can be greatly reduced by introducing this function as a control variate in the computation of the velocity moments. Such a method, even though it can be naturally applied to nonlinear simulations, has originally emerged from linearised simulations and is usually called the delta f particle-in cell (PIC) method. In the past, the method has been extended to also handle collisions. This resulted in a two weight scheme which is known to produce a pronounced weight growth problem which rapidly makes it inefficient as a control variate method for variance reduction. In this work we analyse the weight growth problem within a simple example, which allows us to overcome its pathological behaviour. We also introduce a new split algorithm based on switching the control variate for PIC simulations with collisions. A key element of our algorithm is a new weight smoothing operator which enables us to obtain a significant noise reduction both in the presence of collisions and in the deep nonlinear phase of PIC simulations. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free