Implementation of on-site velocity boundary conditions for D3Q19 lattice Boltzmann simulations

Abstract

On-site boundary conditions are often desired for lattice Boltzmann simulations of fluid flow in complex geometries such as porous media or microfluidic devices. The possibility to specify the exact position of the boundary, independent of other simulation parameters, simplifies the analysis of the system. For practical applications it should allow to freely specify the direction of the flux, and it should be straight forward to implement in three dimensions. Furthermore, especially for parallelized solvers it is of great advantage if the boundary condition can be applied locally, involving only information available on the current lattice site. We meet this need by describing in detail how to transfer the approach suggested by Zou and He [1] to a D3Q19 lattice. The boundary condition acts locally, is independent of the details of the relaxation process during collision and contains no artificial slip. In particular, the case of an on-site no-slip boundary condition is naturally included. We test the boundary condition in several setups and confirm that it is capable to accurately model the velocity field up to second order and does not contain any numerical slip.

Numerical study on the permeability in a tensorial form for laminar flow in anisotropic porous media

“…Again the three variables S, φ, and T were determined independently. Equation (15) seems to agree with the measured and simulated permeability components in this more general case. Although both anisotropy factors α and β were kept larger than one, this represents a general case.…”

“…The results demonstrate that the KC model also describes the permeability tensor K well for the simulated anisotropic media, with the anisotropic nature represented by the tortuosity tensor T [Eq. (15)]. …”

“…15 and 16 are combined with Eq. (15) to obtain the components of the permeability tensor for the case of double anisotropy. This permeability tensor is compared with the values predicted by the simulations in Fig.…”

3D analysis, modeling and simulation of transport processes in compressed fibrous microstructures, using the Lattice Boltzmann method

“…The features of the method range from single phase, single component flow [16,17] to multi component [18,19,20,21] and/or multi phase configurations [18,22,23,24]. Sophisticated data structures and algorithms can be included [25,26] as well as extended boundary conditions [27,22,28]. In this paper we present a LB based method to obtain effective material properties -permeability and tortuosity -of paper type GDLs.…”

One- and two-particle dynamics in microfluidic T-junctions

“…1) has a single inlet with a fluid influx of Q 0 (mass per unit time) and outlets 1 and 2 such that Q 0 (t) = Q 1 (t) + Q 2 (t). We impose no-slip boundary conditions (BCs) at the sidewalls [24] and Poiseuille velocity profiles at the inlet and at the outlets, which are set based on the respective rates of mass flux. To remove reflections, the open boundaries are impedance-matched by requiring (n · ∇) 2 p = 0, wheren is a unit vector normal to the open boundary.…”