Diffused bounce-back condition and refill algorithm for the lattice Boltzmann method

Abstract

A solid-fluid boundary condition for the lattice Boltzmann (LB) method, which retains the simplicity of the bounce-back method and leads to positive definite populations similar to the diffusive boundary condition, is presented. As a refill algorithm, it is proposed that quasi-equilibrium distributions be used to model distributions at fluid nodes uncovered due to solid movement. The method is tested for flow past an impulsively started cylinder and demonstrates considerable enhancement in the accuracy of the unsteady force calculation at moderate and high Reynolds numbers. Furthermore, via simulations, we show that momentum exchange procedure used in LB to compute forces is not Galilean invariant. A modified momentum exchange procedure is proposed to reduce the errors due to violation of Galilean invariance.

Flow force and torque on submerged bodies in lattice-Boltzmann methods via momentum exchange

“…No rigorous proof was presented for these methods. Both [10] and [22] present a similar methods that are based in computing the momentum exchange in a reference frame comoving with the wall.…”

“…We compare results we obtained using a classical ME (20),(30) and the corrected methods given by (22), (32) and (23), (33). These results, particularly those obtained with the corrected methods are in good agreement with tests presented in [3] (obtained using LBM with SI), [9] (obtained using LBM with an expression similar to (22), (32)) and [24] (obtained using FEM).…”

“…Also we implement a method that sets the mentioned variables by using the equilibrium distribution function, where the macroscopic variables are set as an average of the values at the nearest neighbor fluid nodes. The evaluation of the force by (22) we present in Section IV show a short time scale noise. The use of the first two methods mentioned before to initialize the nodes that enter the fluid region present lower noise level.…”

Lattice Boltzmann method used to simulate particle motion in a conduit

“…The action of the particle on the flow is modelled with the help of the hybrid diffused bounce-back condition for the moving boundary, which combines some advantages of the standard bounce-back and of the diffusive boundary condition within the LBM (Krithivasan et al, 2014). Namely, it retains the locality of the bounce-back scheme and smooths populations f i in the immediate surroundings of the moving boundary.…”

“…Lallemand and Luo, 2003) or by the regularized LBM (Latt and Choppard, 2006) or by the so-called entropic LBM (Ansumali and Karlin, 2002;Karlin et al, 2006) -or through the selection of a suitable lattice boundary scheme, as it can substantially influence the solution. In the case of the examined process, the particle Reynolds numbers reach from 10 3 up to 10 4 , and hence a specific lattice boundary scheme is used (Krithivasan et al, 2014). However, modifications of the LBM may also negatively influence either its efficiency or its accuracy.…”