Application of the multi distribution function lattice Boltzmann approach to thermal flows

An improved lattice Boltzmann model is proposed for thermal flows in which the viscous heat dissipation and compression work by the pressure can be neglected. In the improved model, the whole complicated gradient term in the internal energy density distribution function model is correctly discarded by modifying the velocity moments' condition. The corresponding macroscopic energy equation is exactly derived through Chapman–Enskog expansion. In particular, based on the improved thermal model, a double-distribution-function lattice BGK model is developed for two-dimensional Boussinesq flow, which is a typical flow with negligible viscous heat dissipation and compression work. A two-dimensional plane flow and the natural convection of air in a square cavity with various Rayleigh numbers are simulated by using the double-distribution-function lattice BGK model. It is found that there is excellent agreement between the present results with the analytical or benchmark solutions.

Download Full-text

A Double-Distribution-Function Lattice Boltzmann Method for Bed-Load Sediment Transport

International Journal of Applied Mechanics ◽

10.1142/s1758825117500132 ◽

2017 ◽

Vol 09 (01) ◽

pp. 1750013 ◽

Cited By ~ 1

Author(s):

Li Cai ◽

Wenjing Xu ◽

Xiaoyu Luo

Keyword(s):

Distribution Function ◽

Sediment Transport ◽

Lattice Boltzmann Method ◽

Lattice Boltzmann ◽

Distribution Functions ◽

Bed Load ◽

Governing Equations ◽

Function Lattice ◽

Boltzmann Method ◽

Load Sediment

The governing equations of bed-load sediment transport are the shallow water equations and the Exner equation. To embody the advantages of the lattice Boltzmann method (e.g., simplicity, efficiency), the three-velocity (D1Q3) and five-velocity (D1Q5) double-distribution-function lattice Boltzmann models (DDF-LBMs), which can present the numerical solution for one-dimensional bed-load sediment transport, are proposed here based on the quasi-steady approach. The so-called DDF-LBM means we use two distribution functions to describe the movement of the two components, respectively. By using the Chapman–Enskog expansion, the governing equations can be recovered correctly from the DDF-LBMs. To illustrate the efficiency of these, two benchmark tests are used, and excellent agreements between the numerical and analytical solutions are demonstrated. In addition, we show that the D1Q5 DDF-LBM has better accuracy compared to the Hudson’s method.

Download Full-text

Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations

Physical Review E ◽

10.1103/physreve.76.056705 ◽

2007 ◽

Vol 76 (5) ◽

Cited By ~ 75

Author(s):

Q. Li ◽

Y. L. He ◽

Y. Wang ◽

W. Q. Tao

Keyword(s):

Distribution Function ◽

Lattice Boltzmann Method ◽

Lattice Boltzmann ◽

Stokes Equations ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Function Lattice ◽

Boltzmann Method

Download Full-text

Erratum: Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations [Phys. Rev. E76, 056705 (2007)]

Physical Review E ◽

10.1103/physreve.76.069902 ◽

2007 ◽

Vol 76 (6) ◽

Cited By ~ 1

Author(s):

Q. Li ◽

Y. L. He ◽

Y. Wang ◽

W. Q. Tao

Keyword(s):

Distribution Function ◽

Lattice Boltzmann Method ◽

Lattice Boltzmann ◽

Stokes Equations ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Function Lattice ◽

Boltzmann Method

Download Full-text

SIMULATION OF FLUID FLOW AND HEAT TRANSFER IN A PLANE CHANNEL USING THE LATTICE BOLTZMANN METHOD

International Journal of Modern Physics B ◽

10.1142/s0217979203017485 ◽

2003 ◽

Vol 17 (01n02) ◽

pp. 183-187 ◽

Cited By ~ 37

Author(s):

G. H. TANG ◽

W. Q. TAO ◽

Y. L. HE

Keyword(s):

Heat Transfer ◽

Distribution Function ◽

Lattice Boltzmann Method ◽

Lattice Boltzmann ◽

Plane Channel ◽

Parallel Plates ◽

Thermal Boundary Conditions ◽

Flow And Heat Transfer ◽

Forced Convective Flow ◽

Boltzmann Method

Forced convective flow and heat transfer between two parallel plates are studied using the lattice Boltzmann method (LBM) in this paper. Three kinds of thermal boundary conditions at the top and bottom plates are studied. The velocity field is simulated using density distribution function while a separate internal energy distribution function is introduced to simulate the temperature field. The results agree well with data from traditional finite volume method (FVM) and analytical solutions. The present work indicates that LBM may be developed as a promising method for predicting convective heat transfer because of its many inherent advantages.

Download Full-text