Publication Cover
Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 72, 2017 - Issue 6
159
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

Novel hybrid lattice Boltzmann technique with TVD characteristics for simulation of heat transfer and entropy generations of MHD and natural convection in a cavity

ORCID Icon &
Pages 431-449 | Received 10 Aug 2017, Accepted 14 Nov 2017, Published online: 14 Dec 2017

References

  • A. A. Mohamad, Lattice Boltzmann Method: Fundamentals and Engineering Applications with Computer Codes. New York: Springer Science & Business Media, 2011, pp. 1–100.
  • L. F. Richardson, Weather Prediction by Numerical Process. Cambridge: Cambridge University Press, 2007, pp. 1–20.
  • K. W. Morton and D. F. Mayers, Numerical Solution of Partial Differential Equations: An Introduction. Cambridge: Cambridge university press, 2005, pp. 10–15.
  • D. Arumuga Perumal and A. K. Dass, “A review on the development of lattice Boltzmann computation of macro fluid flows and heat transfer,” Alexandria Eng. J., vol. 54, no. 4, pp. 955–971, 2015.
  • U. Frisch, B. Hasslacher, and Y. Pomeau, “Lattice-gas automata for the navier-stokes equation,” Phys. Rev. Lett., vol. 56, no. 14, pp. 1505–1508, 1986.
  • J. Hardy, Y. Pomeau, and O. de Pazzis, “Time evolution of a two-dimensional classical lattice system,” Phys. Rev. Lett., vol. 31, no. 5, pp. 276–279, 1973.
  • G. R. McNamara and G. Zanetti, “Use of the boltzmann equation to simulate lattice-gas automata,” Phys. Rev. Lett., vol. 61, no. 20, pp. 2332–2335, 1988.
  • P. L. Bhatnagar, E. P. Gross, and M. Krook, “A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems,” Phys. Rev., vol. 94, no. 3, pp. 511–525, 1954.
  • J. Koelman, “A simple lattice Boltzmann scheme for Navier-–Stokes fluid flow,” EPL (Europhys. Lett.), vol. 15, no. 6, p. 603, 1991.
  • J. C. Maxwell, “V. Illustrations of the dynamical theory of gases.—Part I. On the motions and collisions of perfectly elastic spheres,” London, Edinburgh, Dublin Philos. Mag. J. Sci., vol. 19, no. 124, pp. 19–32, 1860.
  • O. Filippova and D. Hänel, “Grid refinement for lattice-BGK models,” J. Comput. Phys., vol. 147, no. 1, pp. 219–228, 1998.
  • M. H. Bouzidi, M. Firdaouss, and P. Lallemand, “Momentum transfer of a Boltzmann-lattice fluid with boundaries,” Phys. Fluids, vol. 13, no. 11, pp. 3452–3459, 2001.
  • R. Mei, L.-S. Luo, and W. Shyy, “An accurate curved boundary treatment in the lattice Boltzmann method,” J. Comput. Phys., vol. 155, no. 2, pp. 307–330, 1999.
  • Z. Guo, C. Zheng, and B. Shi, “An extrapolation method for boundary conditions in lattice Boltzmann method,” Phys. Fluids, vol. 14, no. 6, pp. 2007–2010, 2002.
  • Z. Guo and C. Shu, Lattice Boltzmann Method and its Applications in Engineering. Singapore: World Scientific, 2013, pp. 80–120.
  • M. Sukop and D. T. Thorne, Lattice Boltzmann Modeling. New York: Springer, 2006, pp. 50–150.
  • J. D. Anderson and J. Wendt, Computational Fluid Dynamics. New York: Springer, 1995, pp. 1–100.
  • P. Lallemand and L.-S. Luo, “Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy,” Galilean Invar., Stab. Phys. Rev. E, vol. 61, no. 6, pp. 6546–6562, 2000.
  • A. J. Ahrar and M. H. Djavareshkian, “Computational investigation of heat transfer and entropy generation rates of Al2O3 nanofluid with Buongiorno’s model and using a novel TVD hybrid LB method,” J. Mol. Liq., vol. 242, pp. 24–39, 2017.
  • D. d’Humieres, “Generalized lattice-Boltzmann equations,” Prog. Astronaut. Aeronaut., vol. 159, pp. 450–450, 1994.
  • P. J. Dellar, “Incompressible limits of lattice Boltzmann equations using multiple relaxation times,” J. Comput. Phys., vol. 190, no. 2, pp. 351–370, 2003.
  • I. V. Karlin, A. N. Gorban, S. Succi, and V. Boffi, “Maximum entropy principle for lattice kinetic equations,” Phys. Rev. Lett., vol. 81, no. 1, pp. 6–9, 1998.
  • I. V. Karlin, A. Ferrante, and H. C. Öttinger, “Perfect entropy functions of the Lattice Boltzmann method,” EPL (Europhys. Lett.), vol. 47, no. 2, pp. 182, 1999.
  • R. Brownlee, A. N. Gorban, and J. Levesley, “Nonequilibrium entropy limiters in lattice Boltzmann methods,” Phys. A Stat. Mech. Appl., vol. 387, no. 2, pp. 385–406, 2008.
  • A. N. Gorban and D. J. Packwood, “Enhancement of the stability of lattice Boltzmann methods by dissipation control,” Phys. A Stat. Mech. Appl., vol. 414, pp. 285–299, 2014.
  • R. Matin, M. K. Misztal, A. Hernández-García, and J. Mathiesen, “Evaluation of the finite element lattice Boltzmann method for binary fluid flows,” Comput. Math. Appl., vol. 74, no. 2, pp. 281–291, 2017.
  • U. Frisch, D. d’Humieres, B. Hasslacher, P. Lallemand, Y. Pomeau, and J.-P. Rivet, “Lattice gas hydrodynamics in two and three dimensions,” Complex Syst., vol. 1, no. 4, pp. 649–707, 1987.
  • A. Mohamad and A. Kuzmin, “The Soret effect with the D1Q2 and D2Q4 lattice Boltzmann model,” Int. J. Nonlinear Sci. Numer. Simul., vol. 13, no. 3–4, pp. 289–293, 2012.
  • C. Hirsch, Numerical Computation of Internal and External Flows: The Fundamentals of Computational Fluid Dynamics. Oxford: Butterworth-Heinemann, 2007, pp. 150–250.
  • H. K. Versteeg and W. Malalasekera, An Introduction to Computational Fluid Dynamics: The Finite Volume Method. New York: Pearson Education, 2007, pp. 150–250.
  • P. L. Roe, “ Some contributions to the modelling of discontinuous flows,” Large-Scale Computations in Fluid Mechanics, pp. 163–193, 1985.
  • F. Fadaei, A. Molaei Dehkordi, M. Shahrokhi, and Z. Abbasi, “Convective-heat transfer of magnetic-sensitive nanofluids in the presence of rotating magnetic field,” Appl. Therm. Eng., vol. 116, pp. 329–343, 2017.
  • B. P. C. Wan and G. W. Wei, “A new benchmark quality solution for the buoyancy-driven cavity by discrete singular convolution,” Num. Heat Transfer Part B: Fundam., vol. 40, no. 3, pp. 199–228, 2001.
  • G. G. Ilis, M. Mobedi, and B. Sunden, “Effect of aspect ratio on entropy generation in a rectangular cavity with differentially heated vertical walls,” Int. Commun. Heat Mass Transfer, vol. 35, no. 6, pp. 696–703, 2008.
  • D. A. Mayne, A. S. Usmani, and M. Crapper, “H-adaptive finite element solution of high Rayleigh number thermally driven cavity problem,” Int. J. Num. Methods Heat Fluid Flow, vol. 10, no. 6, pp. 598–615, 2000.
  • M. Manzari, “An explicit finite element algorithm for convection heat transfer problems,” Int. J. Num. Methods Heat Fluid Flow, vol. 9, no. 8, pp. 860–877, 1999.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.