Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-10T14:36:31.815Z Has data issue: false hasContentIssue false
  • English
  • Français

Energy Conserving Lattice Boltzmann Models for Incompressible Flow Simulations

Published online by Cambridge University Press:  03 June 2015

Shiwani Singh ,
Siddharth Krithivasan ,
Iliya V. Karlin ,
Sauro Succi  and
Santosh Ansumali
Shiwani Singh*
Affiliation:
Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India
Siddharth Krithivasan*
Affiliation:
Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India
Iliya V. Karlin*
Affiliation:
Aerothermochemistry and Combustion Systems Lab, ETH Zurich, 8092 Zurich, Switzerland Energy Technology Research Group, School of Engineering Sciences, University of Southampton, Southampton, SO171BJ, UK
Sauro Succi*
Affiliation:
Istituto Applicazioni Calcolo “Mauro Picone", C.N.R., Via dei Taurini, 19, 00185, Rome, Italy
Santosh Ansumali*
Affiliation:
Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560064, India
*
Email:shiwani@jncasr.ac.in
Email:siddharth@jncasr.ac.in
Email:ilya.karlin@gmail.com, karlin@lav.mavt.ethz.ch
Email:succi@iac.cnr.it
Corresponding author.Email:ansumali@jncasr.ac.in
Get access

Abstract

In this paper, we highlight the benefits resulting from imposing energy-conserving equilibria in entropic lattice Boltzmann models for isothermal flows. The advantages are documented through a series of numerical simulations, such as Taylor-Green vortices, cavity flow and flow past a sphere.

Keywords

82C40Lattice Boltzmann method
Type
Research Article
Information
Communications in Computational Physics , Volume 13 , Issue 3 , March 2013 , pp. 603 - 613
Copyright
Copyright © Global Science Press Limited 2013

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]Chen, S. and Doolen, G.D.Lattice Boltzmann method for fluid flows. Annual Review of Fluid Mechanics, 30(1): 329, 2003.Google Scholar
[2]Aidun, C.K. and Clausen, J.R.Lattice-Boltzmann method for complex flows. Annual Review of Fluid Mechanics, 42: 439–472, 2010.CrossRefGoogle Scholar
[3]Succi, S., Karlin, I.V., and Chen, H.Colloquium: Role of the H theorem in lattice Boltzmann hydrodynamic simulations. Reviews of Modern Physics, 74(4): 1203–1220, 2002.CrossRefGoogle Scholar
[4]Higuera, FJ. and Jimenez, J.Boltzmann approach to lattice gas simulations. EPL (Euro-physics Letters), 9: 663, 1989.CrossRefGoogle Scholar
[5]Succi, S.The lattice Boltzmann equation for fluid dynamics and beyond. Oxford University Press, USA, 2001.Google Scholar
[6]Espanol, P. and Warren, P.Statistical mechanics of dissipative particle dynamics. EPL (Europhysics Letters), 30:191, 1995.CrossRefGoogle Scholar
[7]Groot, R.D. and Warren, P.B.Dissipative particle dynamics: Bridging the gap between atomistic and mesoscopic simulation. Journal of Chemical Physics, 107(11): 4423, 1997.Google Scholar
[8]Malevanets, A. and Kapral, R.Mesoscopic model for solvent dynamics. Journal of Chemical Physics, 110(17), 1999.Google Scholar
[9]Groot, R.D. and Rabone, K.L.Mesoscopic simulation of cell membrane damage, morphology change and rupture by nonionic surfactants. Biophysical Journal, 81(2): 725–736, 2001.Google Scholar
[10]Noguchi, H. and Gompper, G.Swinging and tumbling of fluid vesicles in shear flow. Physical review letters, 98(12): 128103, 2007.Google Scholar
[11]Ansumali, S., Karlin, I.V., Arcidiacono, S., Abbas, A., and Prasianakis, N.I.Hydrodynamics beyond Navier-Stokes: Exact solution to the Lattice Boltzmann hierarchy. Physical review letters, 98(12): 124502, 2007.Google Scholar
[12]Chen, H., Kandasamy, S., Orszag, S., Shock, R., Succi, S., and Yakhot, V.Extended Boltzmann kinetic equation for turbulent flows. Science, 301(5633): 633, 2003.Google Scholar
[13]Groot, R.D. and Madden, T.J.Dynamic simulation of diblock copolymer microphase separation. The Journal of chemical physics, 108: 8713, 1998.Google Scholar
[14]Benzi, R., Succi, S., and Vergassola, M.The lattice Boltzmann equation: theory and applications. Physics Reports, 222(3): 145–197, 1992.Google Scholar
[15]Higuera, F.J., Succi, S., and Benzi, R.Lattice gas dynamics with enhanced collisions. EPL (Europhysics Letters), 9: 345, 1989.Google Scholar
[16]Karlin, I. V., Ferrante, A., and Ottinger, H. C.Perfect entropy functions of the lattice Boltzmann method. Europhys. Lett., 47: 182–188, 1999.Google Scholar
[17]Wagner, A.J.An H-theorem for the lattice Boltzmann approach to hydrodynamics. EPL (Europhysics Letters), 44: 144, 1998.Google Scholar
[18]Boghosian, B.M., Love, P.J., Coveney, P.V., Karlin, I.V., Succi, S., and Yepez, J.Galilean-invariant lattice-Boltzmann models with H theorem. Physical Review E, 68(2): 025103, 2003.CrossRefGoogle ScholarPubMed
[19]Ansumali, S., Karlin, I. V., and Öttinger, H. C.Minimal entropic kinetic models for simulating hydrodynamics. Europhys. Lett., 63: 798–804, 2003.Google Scholar
[20]Ansumali, S. and Karlin, I.V.Consistent Lattice Boltzmann method. Physical review letters, 95(26): 260605, 2005.CrossRefGoogle ScholarPubMed
[21]Karlin, I. V., Succi, S., and Chikatamarla, S. S.Comment on “numerics of the lattice boltzmann method: Effects of collision models on the lattice boltzmann simulations”. Phys. Rev. E, 84: 068701, Dec 2011.Google Scholar
[22]Asinari, P. and Karlin, I.V.Generalized Maxwell state and H-theorem for the lattice Boltz-mann method. Phys. Rev. E, 79(3): 36703, 2009.Google Scholar
[23]Chikatamarla, S.S. and Karlin, I.V.Entropy and Galilean invariance of lattice Boltzmann theories. Physical review letters, 97(19): 190601, 2006.CrossRefGoogle ScholarPubMed
[24]Nie, X.B., Shan, X., and Chen, H.Galilean invariance of lattice Boltzmann models. EPL (Europhysics Letters), 81: 34005, 2008.Google Scholar
[25]Szalmás, L.Knudsen layer theory for high-order lattice Boltzmann models. EPL (Euro-physics Letters), 80: 24003, 2007.Google Scholar
[26]Shan, X.General solution of lattices for Cartesian lattice Bhatanagar-Gross-Krook models. Physical Review E, 81(3): 036702, 2010.Google Scholar
[27]Yudistiawan, W.P., Kwak, S.K., Patil, D.V., and Ansumali, S.Higher-order Galilean-invariant lattice Boltzmann model for microflows: Single-component gas. Physical Review E, 82(4): 046701, 2010.CrossRefGoogle ScholarPubMed
[28]Nourgaliev, R.R., Dinh, T.N., Theofanous, T.G., and Joseph, D.The lattice Boltzmann equation method: theoretical interpretation, numerics and implications. International Journal of Multiphase Flow, 29(1): 117–169, 2003.Google Scholar
[29]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: 511–525, 1954.Google Scholar
[30]Dellar, P.J.Incompressible limits of lattice Boltzmann equations using multiple relaxation times. Journal of Computational Physics, 190(2): 351–370, 2003.Google Scholar
[31]Dellar, Paul J.Nonhydrodynamic modes and a priori construction of shallow water lattice Boltzmann equations. Phys. Rev. E, 65: 036309, Feb 2002.CrossRefGoogle Scholar
[32]Bruneau, C.H. and Saad, M.The 2d lid-driven cavity problem revisited. Computers & Fluids, 35(3): 326–348, 2006.Google Scholar
[33]Chikatamarla, SS, Ansumali, S., and Karlin, IVGrad’s approximation for missing data in lattice Boltzmann simulations. EPL (Europhysics Letters), 74: 215, 2006.Google Scholar