A numerical scheme that solves the Landau kinetic equation by evolving a system of particles whose pairwise grazing collisions are modeled as diffusion processes. Spherical Brownian-motion sampling lets the discrete-time particle distribution exactly match the continuous-time process without extra temporal discretization, giving O(N) cost per step while exactly conserving mass, momentum and energy and dissipating entropy. Students learn how to design particle discretizations that preserve the physical invariants of a kinetic PDE.
A structure-preserving stochastic particle method for the Landau equation, the kinetic PDE governing the velocity distribution of charged particles in a plasma dominated by grazing (small-angle) coll…