Stability Condition for Single-Relaxation Time Isothermal Lattice Boltzmann Formulation

2014 ◽  
Vol 695 ◽  
pp. 667-670
Author(s):  
Nor Azwadi Che Sidik ◽  
Siti Aisyah Razali
Keyword(s):  
Reynolds Number ◽  
Relaxation Time ◽  
Lattice Boltzmann Method ◽  
Stability Condition ◽  
Lattice Boltzmann ◽  
Mesh Size ◽  
Single Relaxation Time ◽  
The Stability ◽  
Boltzmann Method

In this present research, the Lattice Boltzmann method has been used to determine the stability condition of the single relaxation time. The range of Reynolds number is 100,400 and 1000. Meanwhile, the range of mesh size is varying between 31 to 251. The results show that the increase in both mesh size and Reynolds number give an effect on deviation percentages. The deviation percentages for all mesh and Reynolds number also presented.

Improving the Stability of the Multiple-Relaxation-Time Lattice Boltzmann Method by a Viscosity Counteracting Approach

2015 ◽  
Vol 8 (1) ◽  
pp. 37-51 ◽  
Author(s):  
Chunze Zhang ◽  
Yongguang Cheng ◽  
Shan Huang ◽  
Jiayang Wu
Keyword(s):  
Reynolds Number ◽  
Relaxation Time ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Numerical Instability ◽  
Time Model ◽  
Multiple Relaxation Time ◽  
The Stability ◽  
Boltzmann Method ◽  
Accuracy And Stability

AbstractNumerical instability may occur when simulating high Reynolds number flows by the lattice Boltzmann method (LBM). The multiple-relaxation-time (MRT) model of the LBM can improve the accuracy and stability, but is still subject to numerical instability when simulating flows with large single-grid Reynolds number (Reynolds number/grid number). The viscosity counteracting approach proposed recently is a method of enhancing the stability of the LBM. However, its effectiveness was only verified in the single-relaxation-time model of the LBM (SRT-LBM). This paper aims to propose the viscosity counteracting approach for the multiple-relaxation-time model (MRT-LBM) and analyze its numerical characteristics. The verification is conducted by simulating some benchmark cases: the two-dimensional (2D) lid-driven cavity flow, Poiseuille flow, Taylor-Green vortex flow and Couette flow, and three-dimensional (3D) rectangular jet. Qualitative and Quantitative comparisons show that the viscosity counteracting approach for the MRT-LBM has better accuracy and stability than that for the SRT-LBM.

Simulation of Flow Past a Square Cylinder by Parallel Lattice Boltzmann Method using Multi-Relaxation-Time Scheme

2006 ◽  
Vol 22 (1) ◽  
pp. 35-42 ◽  
Author(s):  
J.-S. Wu ◽  
Y.-L. Shao
Keyword(s):  
Relaxation Time ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Reynolds Numbers ◽  
Numerical Results ◽  
Channel Height ◽  
Blockage Ratio ◽  
Square Cylinder ◽  
Single Relaxation Time ◽  
Boltzmann Method

AbstractThe flows past a square cylinder in a channel are simulated using the multi-relaxation-time (MRT) model in the parallel lattice Boltzmann BGK method (LBGK). Reynolds numbers of the flow are in the range of 100 ∼ 1,850 with blockage ratio, 1/6, of cylinder height to channel height, in which the single-relaxation-time (SRT) scheme is not able to converge at higher Reynolds numbers. Computed results are compared with those obtained using the SRT scheme where it can converge. In addition, computed Strouhal numbers compare reasonably well with the numerical results of Davis (1984).

Reassessing the single relaxation time Lattice Boltzmann method for the simulation of Darcy’s flows

2016 ◽  
Vol 27 (04) ◽  
pp. 1650037 ◽  
Author(s):  
Pietro Prestininzi ◽  
Andrea Montessori ◽  
Michele La Rocca ◽  
Sauro Succi
Keyword(s):  
Porous Media ◽  
Relaxation Time ◽  
Lattice Boltzmann Method ◽  
Knudsen Number ◽  
Lattice Boltzmann ◽  
Physical Dependence ◽  
Single Relaxation Time ◽  
Flows In Porous Media ◽  
Percent Accuracy ◽  
Boltzmann Method

It is shown that the single relaxation time (SRT) version of the Lattice Boltzmann (LB) equation permits to compute the permeability of Darcy’s flows in porous media within a few percent accuracy. This stands in contrast with previous claims of inaccuracy, which we relate to the lack of recognition of the physical dependence of the permeability on the Knudsen number.

Numerical Simulation of Viscous Flow in a 3D Lid-Driven Cavity Using Lattice Boltzmann Method

2013 ◽  
Vol 444-445 ◽  
pp. 395-399
Author(s):  
Di Bo Dong ◽  
Sheng Jun Shi ◽  
Zhen Xiu Hou ◽  
Wei Shan Chen
Keyword(s):  
Reynolds Number ◽  
Viscous Flow ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Three Dimensional ◽  
Primary Vortex ◽  
Driven Cavity ◽  
Single Relaxation Time ◽  
Moderate Reynolds Number ◽  
Boltzmann Method

A lattice Boltzmann method (LBM) with single-relaxation time and on-site boundary condition is used for the simulation of viscous flow in a three-dimensional (3D) lid-driven cavity. Firstly, this algorithm is validated by compared with the benchmark experiments for a standard cavity, and then the results of a cubic cavity with different inflow angles are presented. Steady results presented are for the inflow angle of and, and the Reynolds number is selected as 500. It is found that for viscous flow under moderate Reynolds number, there exists a primary vortex near the center and a secondly vortex at the lower right corner on each slice when, namely in a standard 3D lid-driven cavity, which cant be found when. So it can be thought that the flow pattern in a 3D lid-driven cavity depends not only on the Reynolds number but also the inflow angle.

On the inclusion of mass source terms in a single-relaxation-time lattice Boltzmann method

2018 ◽  
Vol 30 (5) ◽  
pp. 057104 ◽  
Author(s):  
Olav Aursjø ◽  
Espen Jettestuen ◽  
Jan Ludvig Vinningland ◽  
Aksel Hiorth
Keyword(s):  
Relaxation Time ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Source Terms ◽  
Mass Source ◽  
Single Relaxation Time ◽  
Boltzmann Method
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