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Stabilized lattice Boltzmann-Enskog method for compressible flows and its application to one- and two-component fluids in nanochannels

Simone Melchionna1 and Umberto Marini Bettolo Marconi2,*

  • 1CNR-IPCF, Consiglio Nazionale delle Ricerche, Università di Roma La Sapienza, P.le A. Moro 2, 00185 Roma, Italy
  • 2Scuola di Scienze e Tecnologie, Università di Camerino, Via Madonna delle Carceri, 62032 Camerino, INFN Perugia and CNISM, Italy

  • *umberto.marinibettolo@unicam.it
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Phys. Rev. E 85, 036707 – Published 16 March, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.036707

Abstract

A numerically stable method to solve the discretized Boltzmann-Enskog equation describing the behavior of nonideal fluids under inhomogeneous conditions is presented. The algorithm employed uses a Lagrangian finite-difference scheme for the treatment of the convective term and a forcing term to account for the molecular repulsion together with a Bhatnagar-Gross-Krook relaxation term. In order to eliminate the spurious currents induced by the numerical discretization procedure, we use a trapezoidal rule for the time integration together with a version of the two-distribution method of He et al. [J. Comput. Phys. 152, 642 (1999)]. Numerical tests show that, in the case of a one-component fluid in the presence of a spherical potential well, the proposed method reduces the numerical error by several orders of magnitude. We conduct another test by considering the flow of a two-component fluid in a channel with a bottleneck and provide information about the density and velocity field in this structured geometry.

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References (44)

  1. R. Evans, Adv. Phys. 28, 143 (1979).
  2. J. P. Hansen and I. R. McDonald, Theory of Simple Liquids (Academic, Oxford, 1990).
  3. J. Wu and Z. Li, Annu. Rev. Phys. Chem. 58, 85 (2007).
  4. Gad-el-Hak, J. Fluids Eng. 121, 5 (1999).
  5. H. Bruus, Theoretical Microfluidics (Oxford University Press, New York, 2008).
  6. U. Marini Bettolo Marconi, Mol. Phys. 109, 1265 (2011).
  7. S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, 1st ed. (Oxford University Press, New York, 2001).
  8. J. Zhang, Microfluid. Nanofluid. 10, 1 (2001).
  9. S. Ansumali, Commun. Comput. Phys. 9, 1106 (2011).
  10. X. He and L. S. Luo, Phys. Rev. E 55, 6333 (1997).
  11. X. He and L. S. Luo, J. Stat. Phys. 88, 927 (1997).
  12. T. Abe, J. Comput. Phys. 131, 241 (1997).
  13. A. J. Wagner, Int. J. Mod. Phys. B 17, 193 (2003).
  14. X. Shan, Phys. Rev. E 73, 047701 (2006).
  15. M. Sbragaglia, R. Benzi, L. Biferale, S. Succi, K. Sugiyama, and F. Toschi, Phys. Rev. E 75, 026702 (2007).
  16. Z. Guo, C. Zheng, and B. Shi, Phys. Rev. E 83, 036707 (2011).
  17. C. M. Pooley and K. Furtado, Phys. Rev. E 77, 046702 (2008).
  18. J. Zhang and F. Tian, Europhys. Lett. 81, 66005 (2008).
  19. E. S. Kikkinides, A. G. Yiotis, M. E. Kainourgiakis, and A. K. Stubos, Phys. Rev. E 78, 036702 (2008).
  20. E. S. Kikkinides, M. E. Kainourgiakis, A. G. Yiotis, and A. K. Stubos, Phys. Rev. E 82, 056705 (2010).
  21. H. van Beijeren and M. H. Ernst, Physica A 68, 437 (1973); 70, 225 (1973).
  22. J. W. Dufty, A. Santos, and J. J. Brey, Phys. Rev. Lett. 77, 1270 (1996).
  23. A. Santos, J. M. Montanero, J. W. Dufty, and J. J. Brey, Phys. Rev. E 57, 1644 (1998).
  24. J. F. Lutsko, Phys. Rev. Lett. 78, 243 (1997).
  25. J. G. Anero and P. Espanol, Europhys. Lett. 78, 50005 (2007).
  26. X. He, S. Chen, and R. Zhang, J. Comput. Phys. 152, 642 (1999).
  27. T. Lee and C. L. Lin, J. Comput. Phys. 206, 16 (2005); Phys. Rev. E 67, 056703 (2003).
  28. T. Lee and P. F. Fischer, Phys. Rev. E 74, 046709 (2006).
  29. T. Lee, Comput. Math. Appl. 58, 987 (2009).
  30. S. Melchionna and U. Marini Bettolo Marconi, Europhys. Lett. 81, 34001 (2008).
  31. U. Marini Bettolo Marconi and S. Melchionna, J. Phys. Condens. Matter 36, 364110 (2010).
  32. U. Marini Bettolo Marconi and S. Melchionna, J. Chem. Phys. 126, 184109 (2007).
  33. U. Marini Bettolo Marconi and S. Melchionna, J. Chem. Phys. 131, 014105 (2009).
  34. U. Marini Bettolo Marconi and S. Melchionna, J. Chem. Phys. 134, 064118 (2011).
  35. P. L. Bhatnagar, E. P. Gross, and M. Krook, Phys. Rev. 94, 511 (1954).
  36. U. Marini Bettolo Marconi and S. Melchionna, J. Chem. Phys. 135, 044104 (2011).
  37. S. Karni, SIAM J. Sci. Comput. 17, 1019 (1996).
  38. R. Abgrall and S. Karni, J. Comput. Phys. 169, 594 (2001).
  39. D. Moroni, B. Rotenberg, J.-P. Hansen, S. Succi, and S. Melchionna, Phys. Rev. E 73, 066707 (2006).
  40. X. Shan, X.-F. Yuan, and H. Chen, J. Fluid. Mech. 550, 413 (2006).
  41. B. Rotenberg and D. Moroni, Phys. Rev. E 74, 037701 (2006).
  42. Z. Guo, C. Zheng, and B. Shi, Phys. Rev. E 65, 046308 (2002).
  43. P. Bryk, R. Roth, M. Schoen, and S. Dietrich, Europhys. Lett. 63, 233 (2003).
  44. S. Melchionna and U. Marini Bettolo Marconi, Europhys. Lett. 95, 44002 (2011).

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Phys. Rev. E 85, 036707– Published 16 March, 2012
  • Received 12 July 2011

©2012 American Physical Society

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