An accurate treatment of diffuse reflection boundary conditions for a stochastic particle Fokker–Planck algorithm with large time steps

•A stochastic particle algorithm for simulation of flows of wall-confined gases is presented.•The algorithm is constructed for large time steps which reduces the computational cost.•Numerical simulations verify that the proposed algorithm reproduces the correct boundary behaviour.

In this paper, we present a stochastic particle algorithm for the simulation of flows of wall-confined gases with diffuse reflection boundary conditions. Based on the theoretical observation that the change in location of the particles consists of a deterministic part and a Wiener process if the time scale is much larger than the relaxation time, a new estimate for the first hitting time at the boundary is obtained. This estimate facilitates the construction of an algorithm with large time steps for wall-confined flows. Numerical simulations verify that the proposed algorithm reproduces the correct boundary behaviour.