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In this paper, we present a new framework for addressing the nonlinear Landaucollision operator in terms of particle-in-cell methods. We employ theunderlying metriplectic structure of the collision operator and, using a macroparticle discretization for the distribution function, we transform theinfinite-dimensional system into a finite-dimensional time-continuousmetriplectic system for advancing the macro particle weights. Temporaldiscretization is accomplished using the concept of discrete gradients. Theconservation of density, momentum, and energy, as well as the positivesemi-definite production of entropy in both the time-continuous and the fullydiscrete system is demonstrated algebraically. The new algorithm is fullycompatible with the existing particle-in-cell Poisson integrators for theVlasov-Maxwell system.

Metriplectic particle-in-cell integrators for the Landau collision operator