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

Abstract

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.

Enhanced single-node lattice Boltzmann boundary condition for fluid flows

“…Nonequilibrium wall populations. Regarding the approximation of the nonequilibrium component at the wall f eq i (x W , t +1) we can use an approximated nonequilibrium bounce-back [15,17,18]. This is a first-order approximation of the nonequilibrium bounce-back method of Zou and He [34] and it leads to the following second-order accurate approximation:…”

“…Roughly speaking, if we call boundary nodes the nodes located next to the surface, then the boundary condition will need to access the second layer of nodes. Nevertheless, in the past three decades, some local curved boundary conditions have been proposed [10,[14][15][16][17][18][19].…”

“…In the past two decades, few attempts to create local interpolated bounce-back schemes have been proposed [15][16][17][18]20]. A local version of LI was originally proposed to deal with corners using a first-order in time approximation in Ref.…”

“…The remaining local interpolated bounce-back methods [15,17,18] follow a different approach introduced by Chun and Ladd [15]. First, they reconstruct the boundary populations using the wall velocity and a constant approximation for the density.…”

“…However, Chun's and Ladd's method (CL) is not strictly local because, in some situations, it requires information from the second layer of nodes. In the wake of Chun and Ladd, in recent years, two new local boundary conditions have been proposed: Tao et al (NELI-ULT) [17] and Liu et al [18].…”