I will present a conservative discontinuous Galerkin algorithm for particle kinetics on manifolds. The motion of particles on the manifold is represented using a canonical Hamiltonian formulation, allowing the construction of an efficient scheme that conserves particle density and energy exactly. This free streaming update is coupled to a Bhatnagar-Gross-Krook (BGK) collision operator that provides a simplified model for approach to local thermodynamic equilibrium. An iterative scheme is constructed to ensure collisional invariants (density, momentum and energy) are preserved numerically. Rotation is incorporated by modifying the Hamiltonian while retaining the canonical formulation. Several test problems, including Kelvin-Helmholtz instability on the surface of a sphere, demonstrate the successful implementation in the Gkeyll code.
