Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-05-26T03:29:53.016Z Has data issue: false hasContentIssue false
  • English
  • Français

Microflow Simulations via the Lattice Boltzmann Method

Published online by Cambridge University Press:  20 August 2015

Nikolaos Prasianakis  and
Santosh Ansumali
Nikolaos Prasianakis*
Affiliation:
Combustion Research, Paul Scherrer Institute, Villigen PSI 5232, Switzerland
Santosh Ansumali*
Affiliation:
Engineering Mechanics Unit, Jawaharlal Nehru Centre for Scientific Research, JNCASR, 560064 Bangalore, India
*
Corresponding author.Email:nikolaos.prasianakis@psi.ch
Email:ansumali@gmail.com
Get access

Abstract

The exact solution to the hierarchy of nonlinear lattice Boltzmann kinetic equations, for the stationary planar Couette flow for any Knudsen number was presented by S. Ansumali et al. [Phys. Rev. Lett., 98 (2007), 124502]. In this paper, simulation results at a non-vanishing value of the Knudsen number are compared with the closed-form solutions for the higher-order moments. The order of convergence to the exact solution is also studied. The lattice Boltzmann simulations are in excellent agreement with the exact solution.

Keywords

52B1065D1868U0568U07Microflowslattice Boltzmann method
Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 5 , May 2011 , pp. 1128 - 1136
Copyright
Copyright © Global Science Press Limited 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Beskok, A., and Karniadakis, G. E., Microflows: Fundamentals and Simulation, Springer, Berlin, 2001.Google Scholar
[2]Succi, S., The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford University Press, New York, 2001.Google Scholar
[3]Succi, S., Mesoscopic modeling of slip motion at fluid-solid interfaces with heterogeneous catalysis, Phys. Rev. Lett., 89 (2002), 064502.CrossRefGoogle ScholarPubMed
[4]Mognetti, B. M., and Yeomans, J. M., Capillary filling in microchannels patterned by posts, Phys. Rev. E., 80 (2009), 056309.Google Scholar
[5]Sbragaglia, M., and Succi, S., Analytical calculation of slip flow in lattice Boltzmann models with Kinetic boundary conditions, Phys. Fluids., 17 (2005), 093602.Google Scholar
[6]Sbragaglia, M., Benzi, R., Biferale, L., Succi, S., and Toschi, F., Surface roughness-hydrophobicity coupling in microchannel and nanochannel flows, Phys. Rev. Lett., 97 (2006), 204503.Google Scholar
[7]Kunert, C., and Harting, J., Roughness induced boundary slip in microchannel flows, Phys. Rev. Lett., 99 (2007), 176001.Google Scholar
[8]Ansumali, S., and Karlin, I. V., Kinetic boundary conditions in the lattice Boltzmann method, Phys. Rev. E., 66 (2002), 026311.Google Scholar
[9]Ansumali, S., Karlin, I. V., Frouzakis, C. E., and Boulouchos, K. B., Entropic lattice Boltzmann method for simulation of microflows, Phys. A., 359 (2006), 289–305.Google Scholar
[10]Ansumali, S., Karlin, I. V., Arcidiacono, S., Abbas, A., and Prasianakis, N. I., Hydrodynamics beyond Navier-Stokes: exact solution to the lattice Boltzmann hierarchy, Phys. Rev. Lett., 98 (2007), 124502.Google Scholar
[11]Yudistiawan, W. P., Ansumali, S., and Karlin, I. V., Hydrodynamics beyond Navier-Stokes: the slip flow model, Phys. Rev. E., 78 (2008), 016705.Google Scholar
[12]Bhatnagar, P. L., Gross, E. P., and Krook, M., A model for collision processes in gases. I. small amplitude processes in charged and neutral one-component systems, Phys. Rev., 94 (1954), 511–525.Google Scholar
[13]Ansumali, S., Karlin, I. V., and Ottinger, H. C., Minimal entropic Kinetic models for hydrodynamics, Europhys. Lett., 63 (2003), 798–804.Google Scholar
[14]Qian, Y. H., d’Humieres, D., and Lallemand, P., Lattice BGK models for Navier-Stokes equation, Europhys. Lett., 17 (1992), 479–484.CrossRefGoogle Scholar
[15]Kim, S. H., Pitsch, H., and Boyd, I. D., Accuracy of higher-order lattice Boltzmann methods for microscale flows with finite Knudsen numbers, J. Comput. Phys., 227 (2008), 8655–8671.Google Scholar
[16]Ansumali, S., and Karlin, I. V., Consistent lattice Boltzmann methods, Phys. Rev. Lett., 95 (2005), 260605.CrossRefGoogle Scholar