Linearized model Fokker-Planck collision operators for gyrokinetic   simulations. II. Numerical implementation and tests
  A set of key properties for an ideal dissipation scheme in gyrokinetic simulations is proposed, and implementation of a model collision operator satisfying these properties is described. This operator is based on the exact linearized test-particle collision operator, with approximations to the field-particle terms that preserve conservation laws and an H-Theorem. It includes energy diffusion, pitch-angle scattering, and finite Larmor radius effects corresponding to classical (real-space) diffusion. The numerical implementation in the continuum gyrokinetic code GS2 is fully implicit and guarantees exact satisfaction of conservation properties. Numerical results are presented showing that the correct physics is captured over the entire range of collisionalities, from the collisionless to the strongly collisional regimes, without recourse to artificial dissipation. 
M. Barnes, I. G. Abel, W. Dorland, D. R. Ernst, G. W. Hammett, P.   Ricci, B. N. Rogers, A. A. Schekochihin, and T. Tatsuno