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.