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

Thomas Önskog, Jun Zhang

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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.

Original languageEnglish
Pages (from-to)139-146
Number of pages8
JournalPhysica A: Statistical Mechanics and its Applications
Early online date21 Aug 2015
Publication statusPublished - 15 Dec 2015


  • boundary conditions
  • first hitting time
  • Fokker-Planck equation
  • Langevin simulation
  • rarified gas flows
  • stochastic differential equations

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