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

2017 ◽  
Vol 09 (01) ◽  
pp. 1750013 ◽  
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.

A Simplified Lattice Boltzmann Method without Evolution of Distribution Function

2016 ◽  
Vol 9 (1) ◽  
pp. 1-22 ◽  
Author(s):  
Z. Chen ◽  
C. Shu ◽  
Y. Wang ◽  
L. M. Yang ◽  
D. Tan
Keyword(s):  
Distribution Function ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Equilibrium Distribution ◽  
Numerical Test ◽  
Distribution Functions ◽  
Navier Stokes ◽  
Equilibrium Distribution Function ◽  
The Difference ◽  
Boltzmann Method

AbstractIn this paper, a simplified lattice Boltzmann method (SLBM) without evolution of the distribution function is developed for simulating incompressible viscous flows. This method is developed from the application of fractional step technique to the macroscopic Navier-Stokes (N-S) equations recovered from lattice Boltzmann equation by using Chapman-Enskog expansion analysis. In SLBM, the equilibrium distribution function is calculated from the macroscopic variables, while the non-equilibrium distribution function is simply evaluated from the difference of two equilibrium distribution functions. Therefore, SLBM tracks the evolution of the macroscopic variables rather than the distribution function. As a result, lower virtual memories are required and physical boundary conditions could be directly implemented. Through numerical test at high Reynolds number, the method shows very nice performance in numerical stability. An accuracy test for the 2D Taylor-Green flow shows that SLBM has the second-order of accuracy in space. More benchmark tests, including the Couette flow, the Poiseuille flow as well as the 2D lid-driven cavity flow, are conducted to further validate the present method; and the simulation results are in good agreement with available data in literatures.

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

2003 ◽  
Vol 17 (01n02) ◽  
pp. 183-187 ◽  
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.

Numerical Analysis on the Effects of Mixed Convection of Particles Removal Flow over Heated Cavity Using Multi-Relaxation Time Thermal Lattice Boltzmann Method

2014 ◽  
Vol 695 ◽  
pp. 487-490
Author(s):  
Nor Azwadi Che Sidik ◽  
Aman Ali Khan
Keyword(s):  
Distribution Function ◽  
Relaxation Time ◽  
Aspect Ratio ◽  
Mixed Convection ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Numerical Study ◽  
Grashof Number ◽  
Boltzmann Method ◽  
Thermal Lattice Boltzmann

This paper provides numerical study of the effects of mixed convection on particles removal from a cavity using multi-relaxation time thermal lattice Boltzmann method (LBM) for compute the flow and isotherm characteristics in the bottom heated cavity located on a floor of horizontal channel. A point force scheme was applied for particles-fluid interactionand double-distribution function (DFF) was coupled with MRT thermal LBM to study the effects of various grashof number (Gr) and Aspect Ratio (AR) on the efficiency of particles removal. The results show that change in Grashof number and Aspect ratio causes a dramatic different in the flow pattern and particles removal efficiency.

Rayleigh-Taylor Instability Studied With Multi-Relaxation Lattice Boltzmann Method

2013 ◽  
Author(s):  
Saeed J. Almalowi ◽  
Dennis E. Oztekin ◽  
Alparslan Oztekin
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Early Stage ◽  
Density Ratio ◽  
Side Wall ◽  
Immiscible Fluids ◽  
Distribution Functions ◽  
Lattice Arrangement ◽  
Boltzmann Method ◽  
Late Stages

Multi relaxation lattice Boltzmann method is implemented to study Rayleigh-Taylor instabilities. Two immiscible fluids (oil and water) are arrayed into three layers. D2Q9 lattice arrangement for two dimensional computational domains is employed. Density distribution functions for each fluid and distribution functions for the coloring step are determined. The evolution of the interface is identified with the coloring step. Buoyancy and other interaction forces, created by buoyancy, between phases are modeled. Two cases are studied one with periodic boundary condition instead of a side wall, and one bounded on all sides. The study is done with an aspect ratio of two and a density ratio of 1.2. The early and late stages of the instability are characterized. The early stage of both cases shows the initial periodic disturbance being amplified rapidly on the lower interface. The late stages show mushroom-like structures, with significant distortions occurring on the bounded case.

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