A lattice Boltzmann BGK model for simulation of micro flows

2004 ◽  
Vol 67 (4) ◽  
pp. 600-606 ◽  
Author(s):  
X. D Niu ◽  
C Shu ◽  
Y. T Chew
Keyword(s):  
Lattice Boltzmann ◽  
Bgk Model ◽  
Micro Flows

scholarly journals Discrete effect on single-node boundary schemes of lattice Bhatnagar–Gross–Krook model for convection-diffusion equations

2019 ◽  
Vol 31 (01) ◽  
pp. 2050017
Author(s):  
Liang Wang ◽  
Xuhui Meng ◽  
Hao-Chi Wu ◽  
Tian-Hu Wang ◽  
Gui Lu
Keyword(s):  
Boundary Condition ◽  
Relaxation Time ◽  
Lattice Boltzmann ◽  
Diffusion Equations ◽  
Bgk Model ◽  
Distance Ratio ◽  
Single Node ◽  
Convection Diffusion ◽  
Velocity Models ◽  
Discrete Effect

The discrete effect on the boundary condition has been a fundamental topic for the lattice Boltzmann method (LBM) in simulating heat and mass transfer problems. In previous works based on the anti-bounce-back (ABB) boundary condition for convection-diffusion equations (CDEs), it is indicated that the discrete effect cannot be commonly removed in the Bhatnagar–Gross–Krook (BGK) model except for a special value of relaxation time. Targeting this point in this paper, we still proceed within the framework of BGK model for two-dimensional CDEs, and analyze the discrete effect on a non-halfway single-node boundary condition which incorporates the effect of the distance ratio. By analyzing an unidirectional diffusion problem with a parabolic distribution, the theoretical derivations with three different discrete velocity models show that the numerical slip is a combined function of the relaxation time and the distance ratio. Different from previous works, we definitely find that the relaxation time can be freely adjusted by the distance ratio in a proper range to eliminate the numerical slip. Some numerical simulations are carried out to validate the theoretical derivations, and the numerical results for the cases of straight and curved boundaries confirm our theoretical analysis. Finally, it should be noted that the present analysis can be extended from the BGK model to other lattice Boltzmann (LB) collision models for CDEs, which can broaden the parameter range of the relaxation time to approach 0.5.

scholarly journals A Multiple-Grid Lattice Boltzmann Method for Natural Convection under Low and High Prandtl Numbers

Fluids ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 148
Author(s):  
Seyed Amin Nabavizadeh ◽  
Himel Barua ◽  
Mohsen Eshraghi ◽  
Sergio D. Felicelli
Keyword(s):  
Natural Convection ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Large Scale ◽  
Bgk Model ◽  
Flow Equations ◽  
Wide Range ◽  
Prandtl Numbers ◽  
Boltzmann Method ◽  
Benchmark Solutions

A multi-distribution lattice Boltzmann Bhatnagar–Gross–Krook (BGK) model with a multiple-grid lattice Boltzmann (MGLB) model is proposed to efficiently simulate natural convection over a wide range of Prandtl numbers. In this method, different grid sizes and time steps for heat transfer and fluid flow equations are chosen. The model is validated against natural convection in a square cavity, since extensive benchmark solutions are available for that problem. The proposed method can resolve the computational difficulty in simulating problems with very different time scales, in particular, when using extremely low or high Prandtl numbers. The technique can also enhance computational speed and stability while keeping the simplicity of the BGK method. Compared with the conventional lattice Boltzmann method, the simulation time can be reduced up to one-tenth of the time while maintaining the accuracy in an acceptable range. The proposed model can be extended to other lattice Boltzmann collision models and three-dimensional cases, making it a great candidate for large-scale simulations.

Lattice Boltzmann Simulation of Droplet Formation in Non-Newtonian Fluids

2015 ◽  
Vol 17 (4) ◽  
pp. 1056-1072 ◽  
Author(s):  
Y. Shi ◽  
G. H. Tang
Keyword(s):  
Newtonian Fluid ◽  
Power Law ◽  
Lattice Boltzmann ◽  
Droplet Formation ◽  
Continuous Phase ◽  
Droplet Generation ◽  
Bgk Model ◽  
Lattice Boltzmann Simulation ◽  
Power Law Exponent ◽  
Boltzmann Method

AbstractNewtonian and non-Newtonian dispersed phase droplet formation in non-Newtonian continuous phase in T-junction and cross junction microchannels are investigated by the immiscible lattice BGK model. The effects of the non-Newtonian fluid power-law exponent, viscosity and interfacial tension on the generation of the droplet are studied. The final droplet size, droplet generation frequency, and detachment point of the droplet change with the power-law exponent. The results reveal that it is necessary to take into account the non-Newtonian rheology instead of simple Newtonian fluid assumption in numerical simulations. The present analysis also demonstrates that the lattice Boltzmann method is of potential to investigate the non-Newtonian droplet generation in multiphase flow.

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