Conservative discontinuous Galerkin scheme of a gyro-averaged Dougherty collision operator

Abstract

A conservative discontinuous Galerkin scheme for a nonlinear Dougherty collision operator in full-f long-wavelength gyrokinetics is presented. Analytically this model operator has the advective-diffusive form of Fokker-Planck operators, it has a non-decreasing entropy functional, and conserves particles, momentum and energy. Discretely these conservative properties are maintained exactly as well, independent of numerical resolution. In this work the phase space discretization is performed using a novel version of the discontinuous Galerkin scheme, carefully constructed using concepts of weak equality and recovery. Discrete time advancement is carried out with an explicit time-stepping algorithm, whose stability limits we explore. The formulation and implementation within the long-wavelength gyrokinetic solver of Gkeyll are validated with relaxation tests, collisional Landau-damping benchmarks and the study of 5D gyrokinetic turbulence on helical, open field lines.

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• Electromagnetic full-$f$ gyrokinetics in the tokamak edge with discontinuous Galerkin methods
• Improved multispecies Dougherty collisions
• Kinetic modeling of neutral transport for a continuum gyrokinetic code
• Development of Advanced Linearized Gyrokinetic Collision Operators Using a Moment Approach
• Turbulent field fluctuations in gyrokinetic and fluid plasmas
• Turbulent broadening of electron heat-flux width in electromagnetic gyrokinetic simulations of a helical scrape-off layer model
• Conservative DG Method for the Micro-Macro Decomposition of the Vlasov-Poisson-Lenard-Bernstein Model
• Continuum kinetic investigation of the impact of bias potentials in the current saturation regime on sheath formation
• A Parallel-Kinetic-Perpendicular-Moment Model for Magnetized Plasmas
• Reduction of transport due to magnetic shear in gyrokinetic simulations of the scrape-off layer