A SIMPLE METHOD TO CONSTRUCT LOCAL EQUILIBRIUM FUNCTION FOR LATTICE BOLTZMANN METHOD

2013 ◽  
Vol 24 (06) ◽  
pp. 1350038
Author(s):  
P. WANG ◽  
S. Q. ZHANG
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Local Equilibrium ◽  
New Method ◽  
Ratio Test ◽  
Simple Method ◽  
One Dimensional ◽  
Equilibrium Function ◽  
The One ◽  
Boltzmann Method

We have developed a simple method to construct local equilibrium function for lattice Boltzmann method (LBM). This new method can make LBM model satisfy compressible flow with a flexible specific-heat ratio. Test cases, including the one-dimensional Sod flow, one-dimensional Lax flow and thermal Couette flow are presented. Good results obtained using proposed new method, indicate that the proposed method is potentially capable of constructing of the local equilibrium function for LBM.

DEVELOPING LBM-BASED FLUX SOLVER AND ITS APPLICATIONS IN MULTI-DIMENSION SIMULATIONS

2012 ◽  
Vol 19 ◽  
pp. 90-99
Author(s):  
KUN QU ◽  
CHANG SHU ◽  
JINSHENG CAI
Keyword(s):  
Boltzmann Equation ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Lattice Boltzmann Model ◽  
Navier Stokes ◽  
Lattice Boltzmann Equation ◽  
One Dimensional ◽  
Volume Method ◽  
Boltzmann Method ◽  
Boltzmann Model

In this paper, a new flux solver was developed based on a lattice Boltzmann model. Different from solving discrete velocity Boltzmann equation and lattice Boltzmann equation, Euler/Navier-Stokes (NS) equations were solved in this approach, and the flux at the interface was evaluated with a compressible lattice Boltzmann model. This method combined lattice Boltzmann method with finite volume method to solve Euler/NS equations. The proposed approach was validated by some simulations of one-dimensional and multi-dimensional problems.

scholarly journals A Multilevel Finite Difference Scheme for One-Dimensional Burgers Equation Derived from the Lattice Boltzmann Method

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Qiaojie Li ◽  
Zhoushun Zheng ◽  
Shuang Wang ◽  
Jiankang Liu
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Finite Difference Scheme ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
One Dimensional ◽  
Explicit Finite Difference ◽  
Boltzmann Method

An explicit finite difference scheme for one-dimensional Burgers equation is derived from the lattice Boltzmann method. The system of the lattice Boltzmann equations for the distribution of the fictitious particles is rewritten as a three-level finite difference equation. The scheme is monotonic and satisfies maximum value principle; therefore, the stability is proved. Numerical solutions have been compared with the exact solutions reported in previous studies. TheL2, L∞and Root-Mean-Square (RMS) errors in the solutions show that the scheme is accurate and effective.

Numerical Investigation of Unsteady Flows Past Flapping Wings with Immersed Boundary-Lattice Boltzmann Method

2017 ◽  
Vol 34 (2) ◽  
pp. 193-207 ◽  
Author(s):  
C. L. Gong ◽  
Z. J. Yuan ◽  
Q. Zhou ◽  
G. Chen ◽  
Z. Fang
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Flapping Wing ◽  
Flapping Wings ◽  
Immersed Boundary ◽  
Thrust Coefficient ◽  
Single Plate ◽  
The Mean ◽  
The One ◽  
Boltzmann Method

AbstractBiomimetic motions are helpful to underwater vehicles and new conception airplanes design. The lattice Boltzmann method with an immersed boundary method technique is used to reveal the propulsion and lift enhancement mechanism of biomimetic motions. The flow past a sphere and an ellipsoidal flapping wing were validated respectively by comparing with other numerical methods. Then a single flapping wing and three flapping wings in a tandem arrangement are accomplished respectively. It founds that the mean thrust coefficient of three plate wings is bigger than the one of the single plate wing. Three ellipsoidal wings and single ellipsoidal wing are compared. It shows that the single ellipsoidal wing has larger thrust coefficients than the three ellipsoidal wings. Ellipsoidal flapping wing and plate wing were further compared to investigate the influence of wing shape. It indicates the mean thrust coefficient of the ellipsoidal wing is bigger than the plate wing.

scholarly journals One-dimensional transient radiative transfer by lattice Boltzmann method

2013 ◽  
Vol 21 (21) ◽  
pp. 24532 ◽  
Author(s):  
Yong Zhang ◽  
Hongliang Yi ◽  
Heping Tan
Keyword(s):  
Radiative Transfer ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
One Dimensional ◽  
Boltzmann Method

Modeling groundwater flow by lattice Boltzmann method in curvilinear coordinates

2015 ◽  
Vol 26 (02) ◽  
pp. 1550013 ◽  
Author(s):  
Ljubomir Budinski ◽  
Julius Fabian ◽  
Matija Stipic
Keyword(s):  
Groundwater Flow ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Complex Geometry ◽  
Poisson’S Equation ◽  
Curvilinear Coordinates ◽  
Computational Domain ◽  
Poisson's Equation ◽  
Equilibrium Function ◽  
Boltzmann Method

In order to promote the use of the lattice Boltzmann method (LBM) for the simulation of isotropic groundwater flow in a confined aquifer with arbitrary geometry, Poisson's equation was transformed into a curvilinear coordinate system. With the metric function between the physical and the computational domain established, Poisson's equation written in Cartesian coordinates was transformed in curvilinear coordinates. Following, the appropriate equilibrium function for the D2Q9 square lattice has been defined. The resulting curvilinear formulation of the LBM for groundwater flow is capable of modeling flow in domains of complex geometry with the opportunity of local refining/coarsening of the computational mesh corresponding to the complexity of the flow pattern and the required accuracy. Since the proposed form of the LBM uses the transformed equation of flow implemented in the equilibrium function, finding a solution does not require supplementary procedures along the curvilinear boundaries, nor in the zones requiring mesh density adjustments. Thus, the basic concept of the LBM is completely maintained. The improvement of the proposed LBM over the previously published classical methods is completely verified by three examples with analytical solutions. The results demonstrate the advantages of the proposed curvilinear LBM in modeling groundwater flow in complex flow domains.

Lattice Boltzmann Method for Advection and Anisotropic Dispersion Equation

2010 ◽  
Vol 78 (2) ◽  
Author(s):  
Jian Guo Zhou
Keyword(s):  
Lattice Boltzmann Method ◽  
Dispersion Equation ◽  
Lattice Boltzmann ◽  
Simple Procedure ◽  
Local Equilibrium ◽  
Computational Cost ◽  
Equilibrium Distribution Function ◽  
Dispersion Tensor ◽  
Anisotropic Dispersion ◽  
Boltzmann Method

A lattice Boltzmann method is developed for the solution of the advection and anisotropic dispersion equation. In the approach, a novel local equilibrium distribution function is formulated to preserve the advantage of using a single relaxation time for the recovery of the isotropic or anisotropic dispersion tensor in the equation. The method fully retains the innate kinetic features and the simple procedure of the standard lattice Boltzmann method, with an additional benefit of being suitable for rectangular lattices at little extra computational cost. The model has been verified and the results have shown that it can produce accurate solutions with great potential to general advection and dispersion problems, leading to broad applications within a variety of interdisciplinary areas.

scholarly journals Lattice Boltzmann Method Applied to Diffusion in Restructured Heterogeneous Media

2014 ◽  
Vol 354 ◽  
pp. 237-242 ◽  
Author(s):  
E. Walther ◽  
R. Bennacer ◽  
C. Desa
Keyword(s):  
Diffusion Equation ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Heterogeneous Media ◽  
Theoretical Background ◽  
Simple Method ◽  
Equilibrium Distributions ◽  
Boltzmann Method

This paper shows the use of the Lattice Boltzmann Method (LBM) for the simulation of the diffusion equation in complex heterogeneous media. The theoretical background of the method for both homogeneous and heterogeneous media is developed. A simple method to determine the safe use conditions of the LBM is proposed, accompanied by a practical example. The range of interest and condition of non-negativity of the equilibrium distributions are identified for a broad range of diffusive properties ratios.

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