Flow simulations using two dimensional thermal lattice Boltzmann method. (English) Zbl 1244.76100

Almalowi, Saeed J.; Oztekin, Alparslan

J. Appl. Math. 2012, Article ID 135173, 12 p. (2012).

Summary: Lattice Boltzmann method is implemented to study hydrodynamically and thermally developing steady laminar flows in a channel. Numerical simulation of two-dimensional convective heat transfer problem is conducted using two-dimensional, nine directional D2Q9 thermal lattice Boltzmann arrangements. The velocity and temperature profiles in the developing region predicted by lattice Boltzmann method are compared against those obtained by ANSYS-FLUENT. Velocity and temperature profiles as well as the skin friction and the Nusselt numbers agree very well with those predicted by the self-similar solutions of fully developed flows. It is clearly shown here that thermal lattice Boltzmann method is an effective computational fluid dynamics (CFD) tool to study nonisothermal flow problems.

MSC:

76M28

Particle methods and lattice-gas methods

References:

[1]	X. D. Niu, C. Shu, and Y. T. Chew, “A thermal lattice Boltzmann model with diffuse scattering boundary condition for micro thermal flows,” Computers and Fluids, vol. 36, no. 2, pp. 273-281, 2007. · Zbl 1177.76321 · doi:10.1016/j.compfluid.2005.11.007
[2]	S. Chen, D. Martínez, and R. Mei, “On boundary conditions in lattice Boltzmann methods,” Physics of Fluids, vol. 8, no. 9, pp. 2527-2536, 1996. · Zbl 1027.76630 · doi:10.1063/1.869035
[3]	R. Begum and M. A. Basit, “Lattice Boltzmann method and its applications to fluid flow problems,” European Journal of Scientific Research, vol. 22, no. 2, pp. 216-231, 2008.
[4]	Q. Zou and X. He, “On pressure and velocity boundary conditions for the lattice Boltzmann BGK model,” Physics of Fluids, vol. 9, no. 6, pp. 1591-1596, 1997. · Zbl 1185.76873 · doi:10.1063/1.869307
[5]	Y. Shi, T. S. Zhao, and Z. L. Guo, “Finite difference-based lattice Boltzmann simulation of natural convection heat transfer in a horizontal concentric annulus,” Computers and Fluids, vol. 35, no. 1, pp. 1-15, 2006. · Zbl 1134.76440 · doi:10.1016/j.compfluid.2004.11.003
[6]	G. R. McNamara and G. Zanetti, “Use of the boltzmann equation to simulate lattice-gas automata,” Physical Review Letters, vol. 61, no. 20, pp. 2332-2335, 1988. · doi:10.1103/PhysRevLett.61.2332
[7]	M. C. Sukop and D. T. Thorne Jr., Lattice Boltzmann Modeling an Introduction for Geosceintific and Engineers, Springer, Berlin, Germany, 2010.
[8]	A. J. C. Ladd and R. Verberg, “Lattice-Boltzmann simulations of particle-fluid suspensions,” Journal of Statistical Physics, vol. 104, no. 5-6, pp. 1191-1251, 2001. · Zbl 1046.76037 · doi:10.1023/A:1010414013942
[9]	M. Sbragaglia and S. Succi, “Analytical calculation of slip flow in lattice boltzmann models with kinetic boundary conditions,” Physics of Fluids, vol. 17, no. 9, Article ID 093602, 8 pages, 2005. · Zbl 1187.76469 · doi:10.1063/1.2044829
[10]	S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Numerical Mathematics and Scientific Computation, The Clarendon Press/Oxford University Press, New York, NY, USA, 2001. · Zbl 0990.76001
[11]	Q. Liao and T.-C. Jen, “Application of Lattice Boltzmann method in fluid flow and heat transfer,” in Computational Fluid Dynamics Technologies and Applications, InTech.