On a two-relaxation-time D2Q9 lattice Boltzmann model for the Navier–Stokes equations

2018 ◽  
Vol 492 ◽  
pp. 1570-1580 ◽  
Author(s):  
Weifeng Zhao ◽  
Liang Wang ◽  
Wen-An Yong
Keyword(s):  
Relaxation Time ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Lattice Boltzmann Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Boltzmann Model

scholarly journals Simulating Turbulent Buoyant Flow by a Simple LES-Based Thermal Lattice Boltzmann Model

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Sheng Chen
Keyword(s):  
Lattice Boltzmann ◽  
Present Model ◽  
Stokes Equations ◽  
Lattice Boltzmann Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Buoyant Flow ◽  
Eddy Simulation ◽  
Thermal Lattice Boltzmann ◽  
Boltzmann Model

To simulate turbulent buoyant flow in geophysical science, where usually the vorticity-streamfunction equations instead of the primitive-variables Navier-Stokes equations serve as the governing equations, a novel and simple thermal lattice Boltzmann model is proposed based on large eddy simulation (LES). Thanks to its intrinsic features, the present model is efficient and simple for thermal turbulence simulation. Two-dimensional numerical simulations of natural convection in a square cavity were performed at high Rayleigh number varying from 104 to 1010 with Prandtl number at 0.7. The advantages of the present model are validated by numerical experiments.

Lattice Boltzmann Model for Incompressible Axisymmetric Thermal Flows With Swirl

2018 ◽  
Author(s):  
Insaf Mehrez ◽  
Ramla Gheith ◽  
Fethi Aloui ◽  
Samia Ben Nasrallah
Keyword(s):  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Thermal Conditions ◽  
Analytic Solutions ◽  
Lattice Boltzmann Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Wall Boundary Conditions ◽  
Physical Phenomena ◽  
Thermal Flows

This paper presents a Lattice Boltzmann (LB) model for incompressible axisymmetric thermal flows. The forces and source terms are added into the Lattice Boltzmann Equation (LBE) and the incompressible Navier-Stokes equations are recovered by the Chapman-Enskog expansion. The model of Zhou [1] is applied for axial, radial and azimuthal velocities and the model of Q.Li et al [2] is computed for temperature variation. The source term of the scheme is simple and without velocity gradient terms. This approach can solve problems including several physical phenomena and complicated force forms as the flow between two coaxial cylinders. Good agreement is obtained between the present work, the analytic solutions and results of previous studies in cylindrical pipe. It proves the efficiency and simplicity of the proposed model compared to other ones. The Taylor-Couette (TC) system is treated with water flow characterized by a radius ratio η = 0.5 and an aspect ratio Γ = 3.8. Three Reynolds numbers of 85, 100 and 150 are tested. The influence of the end-wall boundary conditions and the influence of thermal conditions on the flow structure and on the temperature distribution along the inner and outer cylinders are analyzed.

A Hybrid Lattice Boltzmann Flux Solver for Simulation of Viscous Compressible Flows

2016 ◽  
Vol 8 (6) ◽  
pp. 887-910 ◽  
Author(s):  
L. M. Yang ◽  
C. Shu ◽  
J. Wu
Keyword(s):  
Lattice Boltzmann ◽  
Compressible Flows ◽  
Stokes Equations ◽  
Strong Shock ◽  
Viscous Flows ◽  
Lattice Boltzmann Model ◽  
Navier Stokes ◽  
Inviscid Flows ◽  
Navier Stokes Equations ◽  
Viscous Compressible Flows

AbstractIn this paper, a hybrid lattice Boltzmann flux solver (LBFS) is proposed for simulation of viscous compressible flows. In the solver, the finite volume method is applied to solve the Navier-Stokes equations. Different from conventional Navier-Stokes solvers, in this work, the inviscid flux across the cell interface is evaluated by local reconstruction of solution using one-dimensional lattice Boltzmann model, while the viscous flux is still approximated by conventional smooth function approximation. The present work overcomes the two major drawbacks of existing LBFS [28–31], which is used for simulation of inviscid flows. The first one is its ability to simulate viscous flows by including evaluation of viscous flux. The second one is its ability to effectively capture both strong shock waves and thin boundary layers through introduction of a switch function for evaluation of inviscid flux, which takes a value close to zero in the boundary layer and one around the strong shock wave. Numerical experiments demonstrate that the present solver can accurately and effectively simulate hypersonic viscous flows.

INCOMPRESSIBLE MRT LATTICE BOLTZMANN MODEL WITH EIGHT VELOCITIES IN 2D SPACE

2009 ◽  
Vol 20 (07) ◽  
pp. 1023-1037 ◽  
Author(s):  
RUI DU ◽  
BAOCHANG SHI
Keyword(s):  
Relaxation Time ◽  
Lattice Boltzmann ◽  
Present Model ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Lattice Boltzmann Model ◽  
Time Model ◽  
Single Relaxation Time ◽  
Double Shear ◽  
Boltzmann Model

In this paper a two-dimensional-eight-velocity lattice Boltzmann model with multi-relaxation-time is proposed for incompressible flows, in which the equilibria in the momentum space are derived from an earlier incompressible lattice Boltzmann model with single relaxation time. Through the Chapman–Enskog expansion, the incompressible Navier–Stokes equations can be recovered. Numerical tests, including the steady Poiseuille flow, the double shear flow and the driven cavity flow, have been carried out to verify the present model. The numerical results agree well with the analytical solutions or the existing results, and it is found that the present model exhibits much better numerical stability than the single relaxation time model.

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