An Alternative Lattice Boltzmann Model for Incompressible Flows and its Stabilization

2017 ◽  
Vol 21 (2) ◽  
pp. 443-465
Author(s):  
Liangqi Zhang ◽  
Zhong Zeng ◽  
Haiqiong Xie ◽  
Zhouhua Qiu ◽  
Liping Yao ◽  
...  
Keyword(s):  
Lattice Boltzmann ◽  
Present Model ◽  
Incompressible Flows ◽  
Hermite Polynomials ◽  
Collision Operator ◽  
Lattice Boltzmann Model ◽  
Navier Stokes ◽  
Equilibrium Distribution Function ◽  
Hydrodynamic Mode ◽  
Diagonal Part

AbstractIn this paper, an alternative lattice Boltzmann (LB)model for incompressible flows is proposed. By modifying directly the moments of the equilibrium distribution function (EDF), the continuous expression of the EDF in tensor Hermite polynomials is derived using the moment expansion and then discretizedwith the discrete velocity vectors of the D2Q9 lattice. The present model as well as its counterpart, the incompressible LB model proposed by Guo, reproduces the incompressible Navier-Stokes (N-S) equations for both steady and unsteady flows. Besides, an alternative pressure formula, which represents the pressure as the diagonal part of the stress tensor, is adopted in the present model. Furthermore, in order to enhance the stability of the present LB model, an additional relaxation time pertaining to the non-hydrodynamic mode is added to the BGK collision operator. The present LB model is validated by two benchmark tests: the cavity flow with different Reynolds number (Re) and the flow past an impulsively started cylinder at Re=40 and 550.

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.

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.

Numerical Simulation of High Reynolds Number Flow Structure in a Lid-Driven Cavity Using MRT-LES

2014 ◽  
Vol 554 ◽  
pp. 665-669
Author(s):  
Leila Jahanshaloo ◽  
Nor Azwadi Che Sidik
Keyword(s):  
Reynolds Number ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Numerical Technique ◽  
Lattice Boltzmann Model ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Driven Cavity ◽  
Reynolds Number Flow ◽  
Boltzmann Method

The Lattice Boltzmann Method (LBM) is a potent numerical technique based on kinetic theory, which has been effectively employed in various complicated physical, chemical and fluid mechanics problems. In this paper multi-relaxation lattice Boltzmann model (MRT) coupled with a Large Eddy Simulation (LES) and the equation are applied for driven cavity flow at different Reynolds number (1000-10000) and the results are compared with the previous published papers which solve the Navier stokes equation directly. The comparisons between the simulated results show that the lattice Boltzmann method has the capacity to solve the complex flows with reasonable accuracy and reliability. Keywords: Two-dimensional flows, Lattice Boltzmann method, Turbulent flow, MRT, LES.

scholarly journals Recovery of Galilean invariance in thermal lattice Boltzmann models for arbitrary Prandtl number

2014 ◽  
Vol 25 (10) ◽  
pp. 1450046 ◽  
Author(s):  
Hudong Chen ◽  
Pradeep Gopalakrishnan ◽  
Raoyang Zhang
Keyword(s):  
Prandtl Number ◽  
Lattice Boltzmann ◽  
Relaxation Times ◽  
Collision Operator ◽  
Lattice Boltzmann Model ◽  
Operator Form ◽  
Prandtl Numbers ◽  
Lattice Boltzmann Models ◽  
Thermal Lattice Boltzmann ◽  
Boltzmann Model

In this paper, we demonstrate a set of fundamental conditions required for the formulation of a thermohydrodynamic lattice Boltzmann model at an arbitrary Prandtl number. A specific collision operator form is then proposed that is in compliance with these conditions. It admits two independent relaxation times, one for viscosity and another for thermal conductivity. But more importantly, the resulting thermohydrodynamic equations based on such a collision operator form is theoretically shown to remove the well-known non-Galilean invariant artifact at nonunity Prandtl numbers in previous thermal lattice Boltzmann models with multiple relaxation times.

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.

Development of Lattice Boltzmann Flux Solver for Simulation of Incompressible Flows

2014 ◽  
Vol 6 (4) ◽  
pp. 436-460 ◽  
Author(s):  
C. Shu ◽  
Y. Wang ◽  
C. J. Teo ◽  
J. Wu
Keyword(s):  
Circular Cylinder ◽  
Lattice Boltzmann ◽  
Incompressible Flows ◽  
Inviscid Flow ◽  
Navier Stokes ◽  
Time Interval ◽  
Uniform Mesh ◽  
Inviscid Flows ◽  
Flow Past ◽  
Flow Variables

AbstractA lattice Boltzmann flux solver (LBFS) is presented in this work for simulation of incompressible viscous and inviscid flows. The new solver is based on Chapman-Enskog expansion analysis, which is the bridge to link Navier-Stokes (N-S) equations and lattice Boltzmann equation (LBE). The macroscopic differential equations are discretized by the finite volume method, where the flux at the cell interface is evaluated by local reconstruction of lattice Boltzmann solution from macroscopic flow variables at cell centers. The new solver removes the drawbacks of conventional lattice Boltzmann method such as limitation to uniform mesh, tie-up of mesh spacing and time interval, limitation to viscous flows. LBFS is validated by its application to simulate the viscous decaying vortex flow, the driven cavity flow, the viscous flow past a circular cylinder, and the inviscid flow past a circular cylinder. The obtained numerical results compare very well with available data in the literature, which show that LBFS has the second order of accuracy in space, and can be well applied to viscous and inviscid flow problems with non-uniform mesh and curved boundary.

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