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Title: Two critical issues in Langevin simulation of gas flows

A stochastic algorithm based on the Langevin equation has been recently proposed to simulate rarefied gas flows. Compared with the direct simulation Monte Carlo (DSMC) method, the Langevin method is more efficient in simulating small Knudsen number flows. While it is well-known that the cell sizes and time steps should be smaller than the mean free path and the mean collision time, respectively, in DSMC simulations, the Langevin equation uses a drift term and a diffusion term to describe molecule movements, so no direct molecular collisions have to be modeled. This enables the Langevin simulation to proceed with a much larger time step than that in the DSMC method. Two critical issues in Langevin simulation are addressed in this paper. The first issue is how to reproduce the transport properties as that described by kinetic theory. Transport coefficients predicted by Langevin equation are obtained by using Green-Kubo formulae. The second issue is numerical scheme with boundary conditions. We present two schemes corresponding to small time step and large time step, respectively. For small time step, the scheme is similar to DSMC method as the update of positions and velocities are uncoupled; for large time step, we present an analytical solutionmore » of the hitting time, which is the crucial factor for accurate simulation. Velocity-Couette flow, thermal-Couette flow, Rayleigh-BĂ©nard flow and wall-confined problem are simulated by using these two schemes. Our study shows that Langevin simulation is a promising tool to investigate small Knudsen number flows.« less
Authors:
 [1] ;  [2]
  1. James Weir Fluids Laboratory, Department of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow G1 1XJ, United Kingdom and State Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences (China)
  2. State Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190 (China)
Publication Date:
OSTI Identifier:
22390543
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1628; Journal Issue: 1; Conference: 29. International Symposium on Rarefied Gas Dynamics, Xi'an (China), 13-18 Jul 2014; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; ANALYTICAL SOLUTION; BOUNDARY CONDITIONS; COLLISIONS; COMPARATIVE EVALUATIONS; COUETTE FLOW; DIFFUSION; KNUDSEN FLOW; KUBO FORMULA; LANGEVIN EQUATION; MEAN FREE PATH; MOLECULES; MONTE CARLO METHOD; STOCHASTIC PROCESSES; VELOCITY