Particulate Flow Simulation via a Boundary Condition-Enforced Immersed Boundary-Lattice Boltzmann Scheme

Abstract

Abstract.A boundary condition-enforced immersed boundary-lattice Boltzmann method (IB-LBM) for the simulation of particulate flows is presented in this paper. In general, the immersed boundary method (IBM) utilizes a discrete set of force density to represent the effect of boundary. In the conventional IB-LBM, such force density is pre-determined, which cannot guarantee exact satisfaction of non-slip boundary condition. In this study, the force density is transferred to the unknown velocity correction which is determined by enforcing the non-slip boundary condition. For the particulate flows, accurate calculation of hydrodynamic force exerted on the boundary of particles is of great importance as it controls the motion of particles. The capability of present method for particulate flows is depicted by simulating migration of one particle in a simple shear flow and sedimentation of one particle in a box and two particles in a channel. The expected phenomena and numerical results are achieved. In addition, particle suspension in a 2D symmetric stenotic artery is also simulated.

Numerical simulation of particle sedimentation in 3D rectangular channel

“…The results showed that, unlike other simulating methods, such as the direct numerical simulation [10] , the finite element method using moving unstructured grids [11] , and the distributed Lagrange multiplier/fictitious domain method [12] , the lattice Boltzmann method was simple, had a more close relationship with the micro scale physics, and its computation cost scaled linearly with the number of the particles [13] . The boundary treatment method is critical in the simulation study of the particulate flow, there are also some improved boundary treatment methods, such as the immersed boundary method [8,[14][15] , which are more accurate for the calculation of the particle fluid interaction. In general, the lattice Boltzmann method is a very promising method for the simulations of particulate flows.…”

Numerical simulation of muco-ciliary clearance: immersed boundary-lattice Boltzmann method

“…Wu and Shu [41] developed a boundary condition enforced IB-LBM. In another investigation, they [36] introduced a new IB-LBM to simulate the migration of a neutrally buoyant particle in the Newtonian flow.…”

“…In the present study we modify the IB-LBM presented by Wu and Shu [36] for the simulation non-Newtonian fluids around immersed boundaries and a new hybrid finite difference-immersed boundary-lattice Boltzmann method (FD-IB-LBM) has been used to study the muco-ciliary transport problem. In this method the main part of the momentum equation (which contains the nonlinear advection term) has been solved by the lattice Boltzmann method (LBM) which is characterized by simple computation, parallel process and easy implementation of boundary conditions.…”

“…This method uses a fixed Cartesian mesh to represent fluid phase, which is composed of Eulerian points. For the boundary immersed in the fluid, a set of Lagrangian points are used to represent it [36] . IB-LBM originally introduced by Feng and Michaelides [38,39] .…”

Particle flow simulation in a channel with symmetric protuberances using combination of lattice Boltzmann and smoothed profile methods

“…Therefore, it is necessary to accurately compute the hydrodynamic force acting on the boundaries of particles. In terms of accuracy in resolving ow eld, it was shown that the boundary condition-enforced IB-LBM provides a simple and accurate way to compute lift and drag (vertical and horizontal) forces exerted on the immersed object [15].…”