Investigation of a side wall heated cavity by using lattice Boltzmann method
DOI:
https://doi.org/10.13052/EJCM.18.217-238Keywords:
lattice Boltzmann method, natural convection, laminar flow, benchmark solution, secondary parameters effectsAbstract
The lattice Boltzmann method based on the BGK model has been used to simulate laminar natural convection in a heated rectangular cavity on the uniform grid. The hydrodynamic and thermal fields are solved by using the double populations approach. A general benchmark has been carried out to show the effects of secondary parameters at their wide range. Excellent agreement is obtained by comparison with available literature.
Downloads
References
Bouzidi M., D’Humières D., Lallemand P., Luo L.S., “Lattice Boltzmann equation on a twodimensional
rectangular grid”, J. Comput. Phys., 172, 2001, p. 704-717.
Bouzidi M., Firdaouss M. and Lallemand P., “Momentum transfer of a Boltzmann-lattice
fluid with boundaries”, Phys. Fluid, 13, 2001, p. 3452-3459.
Chen S. and Doolen G. D., “Lattice Boltzmann method for fluid flows”, Annu. Rev. Fluid
Mech., 30, 1998, p. 329-64.
de Gassowski G., Xin S. et Daube O., « Bifurcations et solutions multiples en cavité 3D différentiellement
chauffée », C. R. Mécanique, 331, 2003, p. 705-711.
de Vahl Davis G., “Natural convection of air in a square cavity: A benchmark numerical
solutions”, Int. J. Numer. Methods Fluids, 3, 1983, p. 249-264.
D’Humières D., Bouzidi M., Lallemand P., “Thirteen-velocity three-dimensional lattice
Boltzmann model”, Phys. Rev. E, 63, 2001, 066702.
Dubois M., Une introduction aux gaz de Boltzmann sur réseau, CNAM, Paris, 2006.
Filippova O. and Hanel D., “Acceleration of Lattice-BGK schemes with grid refinement”,
Journal of Computational Physics, 165, 2000, p. 407-427.
Guo Z. and Zhao T. S., “A Lattice Boltzmann model for convection heat transfer in porous
media”, Numerical Heat Transfer, Part B, 47, 2005, p. 157-177.
Guo Z. and Zhao T. S., “Explicit finite-difference lattice Boltzmann method for curvilinear
coordinates”, Physical Review, E 67, 066709, 2003.
Guo Z., Shi B. and Zheng C., “A coupled lattice BGK model for the Boussinesq equations”,
Int. J. Numer. Meth. Fluids, 39, 2002, p. 325-342.
He X. and Luo L. S., “Lattice Boltzmann model for the incompressible Navier-Stokes equation”,
Journal of Statistical Physics, vol. 88, n° 3/4, 1997.
He X., Zou Q., Luo L. S. and Dembo M., “Analytic Solutions of Simple Flows and Analysis
of Nonslip Boundary Conditions for the Lattice Boltzmann BGK Model”, Journal of Statistical
Physics, vol. 87, n° 1/2, 1997.
Hou S. and Zou Q., “Simulation of cavity flow by the Lattice Boltzmann method”, Journal of
Computational Physics, 118, 1995, p. 329-347.
Ismail K. A. R., Scalon V. L., “A finite element free convection model for the side wall
heated cavity”, Int. J. Heat Mass Transfer 43, 2000, p. 1373-1389.
Jami M., Mezrhab A., Bouzidi M., Lallemand P., “Lattice Boltzmann method applied to the
laminar natural convection in an enclosure with a heat-generating cylinder conducting
body”, International Journal of Thermal Sciences, 46, 2007, p. 38-47.
Kerr R. M. and Herring J. R., “Prandtl number dependence of Nusselt number in DNS”,
J. Fluids Mech, 1999.
Lallemand P., Luo L. S., “Lattice Boltzmann method for moving boundaries”, Journal of
Computational Physics, 184, 2003, p. 406-421.
Mezrhab A., Jami M., Bouzidi M. and Lallemand P., “Analysis of radiation-natural convection
in a divided enclosure using the lattice Boltzmann method”, Computers and fluids,
, n° 2, 2007, p. 423-434.
Mohamad A. A., Applied Lattice Boltzmann Method for Transport Phenomena, Momentum,
Heat and Mass Transfer, 2007.
Ozoe H., Sayama H., “Natural convection in an inclined rectangular channel at various aspect
ratios and angles-Experimental measurements”, Int. J. Heat Mass transfer, vol. 18, 1975,
p. 1425-1431.
Paolucci S. and Chennoweth D. R., “Transition to chaos in a differentially heated vertical
cavity”, J. Fluid Mech., vol. 201, 1989, p. 379-410.
Peng Y., Shu C., Chew Y. T., “Simplified thermal lattice Boltzmann model for incompressible
thermal flows”, Phys. Rev., E, 68, 026701, 2003, p. 1-8.
Qian Y. H., D’Humieres D. and Lallemand P., “Lattice BGK Models for Navier-Stokes Equation”,
Europhys. Lett., vol. 17, n° 6, 1992, p. 479-484.
Succi S., The lattice Boltzmann equation for fluid dynamics and beyond, Italy, 2001, p. 15
Semma E., El Ganaoui M., Bennacer R., Mohamad A. A., “Investigation of flows in
solidification by using the lattice Boltzmann method”, International Journal of Thermal
Sciences, 47, 2008, p. 201-208.
Shu C. and Xue h., “Comparison of two approaches for implementing stream function boundary
condition in DQ simulation of natural convection in square cavity”, Int. J. Heat and
Fluid Flow, 19, 1998, p. 59-68.
Shu C., Niu X.D., Peng Y. and Chew Y.T., “Taylor series expansion-and least square-based
Lattice Boltzmann method: an efficient approach for simulation of incompressible viscous
flows”, Progress in Computational Fluid Dynamics, vol. 5, 2005, Nos. 1/2.
Shu C., Peng Y., and Chew Y. T., “Simulation of natural convection in square cavity by
Taylor series expansion-and least square-based lattice Boltzmann method”, International
Journal of Modern Physics C, vol. 13, n° 10, 2002, p. 1399-1414.
Sukop M. C., Thorne Daniel T., Lattice Boltzmann modelling, an introduction for Geoscientists
and engineers, Florida USA, 2005
Vahala G., Pavlo P., Vahala L. and Martys N. S., “Thermal Lattice Boltzmann Model
(TLBM) for compressible flows”, International Journal for Modern Physics C, vol. 9,
, n° 8, p. 1247-1261.
Zou Q. and He X., “On pressure and velocity boundary conditions for the lattice Boltzmann
BGK model”, Phys. Fluids, vol. 9, n° 6, 1997.