Assessment of algorithms for the no-slip boundary condition in the lattice Boltzmann equation of BGK model

2008 ◽  
Vol 58 (12) ◽  
pp. 1353-1378 ◽  
Author(s):  
Yong Kweon Suh ◽  
Jinfen Kang ◽  
Sangmo Kang
Keyword(s):  
Boundary Condition ◽  
Boltzmann Equation ◽  
Lattice Boltzmann ◽  
Slip Boundary Condition ◽  
Lattice Boltzmann Equation ◽  
Bgk Model ◽  
Slip Boundary

scholarly journals Involving the Navier–Stokes equations in the derivation of boundary conditions for the lattice Boltzmann method

2011 ◽  
Vol 369 (1944) ◽  
pp. 2184-2192 ◽  
Author(s):  
Joris C. G. Verschaeve
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Grid Spacing ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Boltzmann Method

By means of the continuity equation of the incompressible Navier–Stokes equations, additional physical arguments for the derivation of a formulation of the no-slip boundary condition for the lattice Boltzmann method for straight walls at rest are obtained. This leads to a boundary condition that is second-order accurate with respect to the grid spacing and conserves mass. In addition, the boundary condition is stable for relaxation frequencies close to two.

Examination of the Slip Boundary Condition by µ-PIV and Lattice Boltzmann Simulations

2002 ◽  
Author(s):  
Derek C. Tretheway ◽  
Luoding Zhu ◽  
Linda Petzold ◽  
Carl D. Meinhart
Keyword(s):  
Boundary Condition ◽  
Shear Rate ◽  
Channel Flow ◽  
Lattice Boltzmann ◽  
Slip Velocity ◽  
Slip Length ◽  
Slip Boundary Condition ◽  
Slip Boundary ◽  
Lattice Boltzmann Simulations ◽  
Bounce Back

This work examines the slip boundary condition by Lattice Boltzmann simulations, addresses the validity of the Navier’s hypothesis that the slip velocity is proportional to the shear rate and compares the Lattice Boltzmann simulations to the experimental results of Tretheway and Meinhart (Phys. of Fluids, 14, L9–L12). The numerical simulation models the boundary condition as the probability, P, of a particle to bounce-back relative to the probability of specular reflection, 1−P. For channel flow, the numerically calculated velocity profiles are consistent with the experimental profiles for both the no-slip and slip cases. No-slip is obtained for a probability of 100% bounce-back, while a probability of 0.03 is required to generate a slip length and slip velocity consistent with the experimental results of Tretheway and Meinhart for a hydrophobic surface. The simulations indicate that for microchannel flow the slip length is nearly constant along the channel walls, while the slip velocity varies with wall position as a results of variations in shear rate. Thus, the resulting velocity profile in a channel flow is more complex than a simple combination of the no-slip solution and slip velocity as is the case for flow between two infinite parallel plates.

A New Partial Slip Boundary Condition for the Lattice-Boltzmann Method

2013 ◽  
Author(s):  
Marc-Florian Uth ◽  
Alf Crüger ◽  
Heinz Herwig
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Slip Model ◽  
Navier Stokes Equations ◽  
Navier Slip ◽  
Slip Boundary ◽  
Boltzmann Method

In micro or nano flows a slip boundary condition is often needed to account for the special flow situation that occurs at this level of refinement. A common model used in the Finite Volume Method (FVM) is the Navier-Slip model which is based on the velocity gradient at the wall. It can be implemented very easily for a Navier-Stokes (NS) Solver. Instead of directly solving the Navier-Stokes equations, the Lattice-Boltzmann method (LBM) models the fluid on a particle basis. It models the streaming and interaction of particles statistically. The pressure and the velocity can be calculated at every time step from the current particle distribution functions. The resulting fields are solutions of the Navier-Stokes equations. Boundary conditions in LBM always not only have to define values for the macroscopic variables but also for the particle distribution function. Therefore a slip model cannot be implemented in the same way as in a FVM-NS solver. An additional problem is the structure of the grid. Curved boundaries or boundaries that are non-parallel to the grid have to be approximated by a stair-like step profile. While this is no problem for no-slip boundaries, any other velocity boundary condition such as a slip condition is difficult to implement. In this paper we will present two different implementations of slip boundary conditions for the Lattice-Boltzmann approach. One will be an implementation that takes advantage of the microscopic nature of the method as it works on a particle basis. The other one is based on the Navier-Slip model. We will compare their applicability for different amounts of slip and different shapes of walls relative to the numerical grid. We will also show what limits the slip rate and give an outlook of how this can be avoided.

Slip boundary condition for lattice Boltzmann modeling of liquid flows

2018 ◽  
Vol 161 ◽  
pp. 60-73 ◽  
Author(s):  
Kai Wang ◽  
Zhenhua Chai ◽  
Guoxiang Hou ◽  
Wei Chen ◽  
Sheng Xu
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann ◽  
Slip Boundary Condition ◽  
Slip Boundary ◽  
Lattice Boltzmann Modeling ◽  
Liquid Flows

ELECTROKINETIC SLIP FLOW OF MICROFLUIDICS IN TERMS OF STREAMING POTENTIAL BY A LATTICE BOLTZMANN METHOD: A BOTTOM-UP APPROACH

2007 ◽  
Vol 18 (04) ◽  
pp. 693-700 ◽  
Author(s):  
XIN FU ◽  
BAOMING LI ◽  
JUNFENG ZHANG ◽  
FUZHI TIAN ◽  
DANIEL Y. KWOK
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Slip Boundary ◽  
Surface Energetics ◽  
Boltzmann Method

In traditional computational fluid dynamics, the effect of surface energetics on fluid flow is often ignored or translated into an arbitrary selected slip boundary condition in solving the Navier-Stokes equation. Using a bottom-up approach, we show in this paper that variation of surface energetics through intermolecular theory can be employed in a lattice Boltzmann method to investigate both slip and non-slip phenomena in microfluidics in conjunction with the description of electrokinetic phenomena for electrokinetic slip flow. Rather than using the conventional Navier-Stokes equation with a slip boundary condition, the description of electrokinetic slip flow in microfluidics is manifested by the more physical solid-liquid energy parameters, electrical double layer and contact angle in the mean-field description of the lattice Boltzmann method.

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