An Improved Particle Scheme for Solving Fokker-Planck Models of the Boltzmann Equation

Abstract This paper presents an improved particle scheme for solving Fokker-Planck models of the Boltzmann equation. The proposed method employs a second-order Strang splitting scheme for accurate time integration. Element-wise basis functions are chosen for spatial discretization, and the moments of the distribution function are calculated by projection onto these basis functions. The method is validated using a 1D Couette flow test case, demonstrating its temporal and spatial convergence properties. The results show that the proposed scheme provides accurate solutions for the Boltzmann equation with the Ellipsoidal-Statistical Fokker-Planck collision operator.