Explicit Fokker--Planck collision operators impose very small timesteps in collisional gyrokinetic scrape-off-layer simulations. This work implements a Bhatnagar--Gross--Krook (BGK) operator in Gkeyll's discontinuous Galerkin full-$f$ solver, treating collisionless advection explicitly and collisions with backward Euler. A fixed-point correction adjusts the discrete Maxwellian so density, momentum, and energy moments are conserved to near machine precision; the formulation also supports cross-species collisions. Benchmarks against the more detailed Lenard--Bernstein--Dougherty (LBD) operator cover shock relaxation, anisotropic interspecies equilibration, and a two-dimensional axisymmetric ASDEX Upgrade SOL. At converged resolution, BGK and LBD produce similar steady density, temperature, potential, and heat-flux profiles. The BGK scheme is more robust at lower resolution, yielding a net
- Implemented an implicit BGK collision operator for Gkeyll's discontinuous Galerkin gyrokinetic solver.
- Enforced discrete density, momentum, and energy conservation through iterative Maxwellian correction.
- Extended the implicit and conservative formulation to cross-species collisions.
- Validated the operator against LBD results in relaxation tests and an ASDEX Upgrade SOL simulation.
- Achieved a
$56\times$ end-to-end speedup by combining larger timesteps with lower-resolution convergence.