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

Thomas Önskog; Jun Zhang

doi:10.1016/j.physa.2015.07.003

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

Thomas Önskog^*, Jun Zhang

^*Corresponding author for this work

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Abstract

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 language	English
Pages (from-to)	139-146
Number of pages	8
Journal	Physica A: Statistical Mechanics and its Applications
Volume	440
Early online date	21 Aug 2015
DOIs	https://doi.org/10.1016/j.physa.2015.07.003
Publication status	Published - 15 Dec 2015

Keywords

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

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10.1016/j.physa.2015.07.003

Onskog-Zhang-PASMA-An-accurate-treatment-of-diffuse-reflection-boundary-conditions-for-a-stochasticAccepted author manuscript, 149 KBLicence: CC BY-NC-ND 4.0

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

abstract = "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.",

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T1 - An accurate treatment of diffuse reflection boundary conditions for a stochastic particle Fokker-Planck algorithm with large time steps

AU - Önskog, Thomas

AU - Zhang, Jun

PY - 2015/12/15

Y1 - 2015/12/15

N2 - 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.

AB - 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.

KW - boundary conditions

KW - first hitting time

KW - Fokker-Planck equation

KW - Langevin simulation

KW - rarified gas flows

KW - stochastic differential equations

UR - http://www.scopus.com/inward/record.url?scp=84941242089&partnerID=8YFLogxK

UR - http://www.sciencedirect.com/science/article/pii/S0378437115006123

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DO - 10.1016/j.physa.2015.07.003

M3 - Article

AN - SCOPUS:84941242089

SN - 0378-4371

VL - 440

SP - 139

EP - 146

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

ER -

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

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