Abstract
| Language | English |
|---|---|
| Title of host publication | Rarefied Gas Dynamics 2014 |
| Subtitle of host publication | Proceedings of the 29th International Symposium on Rarefied Gas Dynamics |
| Pages | 1087-1094 |
| Number of pages | 8 |
| Volume | 1328 |
| DOIs | |
| Publication status | Published - Sep 2014 |
| Event | 29th International Symposium on Rarefied Gas Dynamics - Hilton Xi’an Hotel, Xi'an, China Duration: 13 Jul 2014 → 18 Jul 2014 |
Publication series
| Name | AIP Conference Proceedings |
|---|---|
| Publisher | American Institute of Physics |
| Volume | 1328 |
Conference
| Conference | 29th International Symposium on Rarefied Gas Dynamics |
|---|---|
| Country | China |
| City | Xi'an |
| Period | 13/07/14 → 18/07/14 |
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Keywords
- Langevin dynamics
- Fokker-Planck equation
- transport properties
- DSMC method
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Two critical issues in Langevin simulation of gas flows. / Zhang, Jun.
Rarefied Gas Dynamics 2014: Proceedings of the 29th International Symposium on Rarefied Gas Dynamics. Vol. 1328 2014. p. 1087-1094 (AIP Conference Proceedings; Vol. 1328).Research output: Chapter in Book/Report/Conference proceeding › Chapter (peer-reviewed)
TY - CHAP
T1 - Two critical issues in Langevin simulation of gas flows
AU - Zhang, Jun
PY - 2014/9
Y1 - 2014/9
N2 - 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 solution of the hitting time, which is the crucial factor for accurate simulation. Velocity-Couette flow, thermal-Couette flow, Rayleigh-Bénard 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.
AB - 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 solution of the hitting time, which is the crucial factor for accurate simulation. Velocity-Couette flow, thermal-Couette flow, Rayleigh-Bénard 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.
KW - Langevin dynamics
KW - Fokker-Planck equation
KW - transport properties
KW - DSMC method
UR - http://rgd29.org/wordpress/wp-content/uploads/2014/12/RGD29-Proceedings.Table-of-Contents.pdf
U2 - 10.1063/1.4902714
DO - 10.1063/1.4902714
M3 - Chapter (peer-reviewed)
SN - 978-0-7354-1265-1
VL - 1328
T3 - AIP Conference Proceedings
SP - 1087
EP - 1094
BT - Rarefied Gas Dynamics 2014
ER -