scholarly journals Reviving the local second-order boundary approach within the two-relaxation-time lattice Boltzmann modelling

2020 ◽  
Vol 378 (2175) ◽  
pp. 20190404 ◽  
Author(s):  
Goncalo Silva ◽  
Irina Ginzburg
Keyword(s):  
Boundary Condition ◽  
Relaxation Time ◽  
Cross Sections ◽  
Lattice Boltzmann ◽  
Soft Matter ◽  
Second Order ◽  
Unknown Boundary ◽  
Single Node ◽  
Finite Difference Approximations ◽  
Problem Class

This work addresses the Dirichlet boundary condition for momentum in the lattice Boltzmann method (LBM), with focus on the steady-state Stokes flow modelling inside non-trivial shaped ducts. For this task, we revisit a local and highly accurate boundary scheme, called the local second-order boundary (LSOB) method. This work reformulates the LSOB within the two-relaxation-time (TRT) framework, which achieves a more standardized and easy to use algorithm due to the pivotal parametrization TRT properties. The LSOB explicitly reconstructs the unknown boundary populations in the form of a Chapman–Enskog expansion, where not only first- but also second-order momentum derivatives are locally extracted with the TRT symmetry argument, through a simple local linear algebra procedure, with no need to compute their non-local finite-difference approximations. Here, two LSOB strategies are considered to realize the wall boundary condition, the original one called Lwall and a novel one Lnode, which operate with the wall and node variables, roughly speaking. These two approaches are worked out for both plane and curved walls, including the corners. Their performance is assessed against well-established LBM boundary schemes such as the bounce-back, the local second-order accurate CLI scheme and two different parabolic multi-reflection (MR) schemes. They are all evaluated for 3D duct flows with rectangular, triangular, circular and annular cross-sections, mimicking the geometrical challenges of real porous structures. Numerical tests confirm that LSOB competes with the parabolic MR accuracy in this problem class, requiring only a single node to operate. This article is part of the theme issue ‘Fluid dynamics, soft matter and complex systems: recent results and new methods’.

scholarly journals Discrete effect on single-node boundary schemes of lattice Bhatnagar–Gross–Krook model for convection-diffusion equations

2019 ◽  
Vol 31 (01) ◽  
pp. 2050017
Author(s):  
Liang Wang ◽  
Xuhui Meng ◽  
Hao-Chi Wu ◽  
Tian-Hu Wang ◽  
Gui Lu
Keyword(s):  
Boundary Condition ◽  
Relaxation Time ◽  
Lattice Boltzmann ◽  
Diffusion Equations ◽  
Bgk Model ◽  
Distance Ratio ◽  
Single Node ◽  
Convection Diffusion ◽  
Velocity Models ◽  
Discrete Effect

The discrete effect on the boundary condition has been a fundamental topic for the lattice Boltzmann method (LBM) in simulating heat and mass transfer problems. In previous works based on the anti-bounce-back (ABB) boundary condition for convection-diffusion equations (CDEs), it is indicated that the discrete effect cannot be commonly removed in the Bhatnagar–Gross–Krook (BGK) model except for a special value of relaxation time. Targeting this point in this paper, we still proceed within the framework of BGK model for two-dimensional CDEs, and analyze the discrete effect on a non-halfway single-node boundary condition which incorporates the effect of the distance ratio. By analyzing an unidirectional diffusion problem with a parabolic distribution, the theoretical derivations with three different discrete velocity models show that the numerical slip is a combined function of the relaxation time and the distance ratio. Different from previous works, we definitely find that the relaxation time can be freely adjusted by the distance ratio in a proper range to eliminate the numerical slip. Some numerical simulations are carried out to validate the theoretical derivations, and the numerical results for the cases of straight and curved boundaries confirm our theoretical analysis. Finally, it should be noted that the present analysis can be extended from the BGK model to other lattice Boltzmann (LB) collision models for CDEs, which can broaden the parameter range of the relaxation time to approach 0.5.

The LBE Simulation and PIV Experimental Study on a Novel Viscous Pump

2005 ◽  
Author(s):  
Fan Yang ◽  
Shuhong Liu ◽  
Jinwei Li ◽  
Yulin Wu
Keyword(s):  
Boundary Condition ◽  
Unsteady Flow ◽  
Cross Sections ◽  
Lattice Boltzmann ◽  
Moving Boundary ◽  
Flow Problem ◽  
Numerical Study ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Moving Boundary Condition

A numerical study and PIV investigation of flow in a novel viscous-based pumping device appropriate for microscale applications is described. The device, essentially consisting of a rotating cylinder eccentrically placed in a channel, is shown to be capable of generating a net flow. The two shape cross-sections of cylinders, the circular and four semi-elliptic lobed contour are studied, which is the steady and unsteady flow problem, respectively. The lattice Boltzmann equation (LBE) simulations at low Reynolds numbers are carried out to study the influence of various geometric parameters, which the results are compared with the PIV experiment ones. The unified solid curved wall boundary condition based on interpolation and the balance of momentum on the wall of the LBE simulation is used in steady and unsteady flow, and the moving boundary condition is also used in the latter. The numerical results indicated that the more effective pumping and better performance is obtained with the decrease of Reynolds number, as well as the increase regular degree of cylinder cross-section.

Lattice Boltzmann simulation of particle-laden flows using an improved curved boundary condition

2019 ◽  
Vol 30 (06) ◽  
pp. 1950041
Author(s):  
Shasha Liu ◽  
Taotao Zhou ◽  
Shi Tao ◽  
Zhibin Wu ◽  
Guang Yang
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann ◽  
Boundary Surface ◽  
Second Order ◽  
Solid Boundary ◽  
Local Computation ◽  
Order Accuracy ◽  
Nonequilibrium Distribution ◽  
Present Scheme ◽  
Curved Boundary

In the application of the lattice Boltzmann method (LBM) for the simulation of the interface-resolved particulate flows, the bounce-back (BB) type rules have been widely adopted to handle the complex boundaries of moving particle. However, the original method cannot preserve the integrity of the particle shape, resulting in a low-resolution for the flow description near the solid boundary. Even though the subsequent modified BB scheme, i.e. the curved boundary condition (CBC), improves the overall accuracy, it generally loses the local-computation property of the simple BB. Therefore, a CBC is proposed in this paper, which maintains the two advantages of the second-order accuracy and local computation in the boundary treatment simultaneously. In the present scheme, information of only a single fluid point is needed. Furthermore, the relative distance between the fluid point and the boundary surface is involved, contributing to the second-order accuracy that is validated in the Poiseuille and cylindrical Couette flows. Particularly, it is found that the precision of the present scheme can be greatly improved with the nonequilibrium distribution functions of two directions included. Three more test cases of particle-laden flow, including particle migration in a channel, the sedimentation of a particle under gravity and the drafting-kissing-tumbling (DKT) dynamics of two settling particles, further demonstrate the feasibility and accuracy of the present scheme.

scholarly journals Enhanced single-node lattice Boltzmann boundary condition for fluid flows

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Francesco Marson ◽  
Yann Thorimbert ◽  
Bastien Chopard ◽  
Irina Ginzburg ◽  
Jonas Latt
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann ◽  
Fluid Flows ◽  
Single Node

First- and second-order forcing expansions in a lattice Boltzmann method reproducing isothermal hydrodynamics in artificial compressibility form

2012 ◽  
Vol 698 ◽  
pp. 282-303 ◽  
Author(s):  
Goncalo Silva ◽  
Viriato Semiao
Keyword(s):  
Relaxation Time ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Order Term ◽  
Second Order ◽  
Navier Stokes ◽  
Forcing Term ◽  
Boltzmann Method

AbstractThe isothermal Navier–Stokes equations are determined by the leading three velocity moments of the lattice Boltzmann method (LBM). Necessary conditions establishing the hydrodynamic consistency of these moments are provided by multiscale asymptotic techniques, such as the second-order Chapman–Enskog expansion. However, for simulating incompressible hydrodynamics the structure of the forcing term in the LBM is still a discordant issue as far as its correct velocity expansion order is concerned. This work uses the traditional second-order Chapman–Enskog expansion analysis to demonstrate that the truncation order of the forcing term may depend on the time regime in this case. This is due to the fact that LBM does not reproduce exactly the incompressibility condition. It rather approximates it through a weakly compressible or an artificial compressible system. The present study shows that for the artificial compressible setup, as the incompressibility flow condition is singularly perturbed by the time variable, such a connection will also affect the LBM forcing formulation. As a result, for time-independent incompressible flows the LBM forcing must be truncated to first order whereas for a time-dependent case it is convenient to include the second-order term. The theoretical findings are confirmed by numerical tests carried out in several distinct benchmark flows driven by space- and/or time-varying body forces and possessing known analytical solutions. These results are verified for the single relaxation time, the multiple relaxation time and the regularized collision models.

An alternative second order scheme for curved boundary condition in lattice Boltzmann method

2015 ◽  
Vol 114 ◽  
pp. 193-202 ◽  
Author(s):  
Liangqi Zhang ◽  
Zhong Zeng ◽  
Haiqiong Xie ◽  
Xutang Tao ◽  
Yongxiang Zhang ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Second Order ◽  
Curved Boundary ◽  
Order Scheme ◽  
Boltzmann Method
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