Full-scale solutions to particle-laden flows: Multidirect forcing and immersed boundary method

Abstract

Towards getting the full-scale solutions to particle-laden flows, a multidirect forcing technique and immersed boundary method are proposed in the present work. The immersed solid boundary is represented by Lagrangian points and the no-slip condition is efficiently satisfied by exerting multidirect forcing. The hydrodynamic interactions between the stationary or moving solid boundary and the Newtonian fluid are able to be accurately described. This method is simple but efficient which is validated by simulating the flows around a stationary circular disc at different Reynolds numbers and the free sedimentation of a particle. The predicted results agree well with previous experimental and numerical data. When applying this method to study particle sedimentation near a vertical wall, the rotation shifting phenomenon is observed besides the anomalous rolling and the lateral migration.

A comparative study of direct‐forcing immersed boundary‐lattice Boltzmann methods for stationary complex boundaries

“…For the implicit diffuse interface scheme, we adopt the multi-direct-forcing method proposed by Luo et al [27] and Wang et al [19] in order to avoid the calculation of complicated banded matrix equations as in [25,26,34]. The calculation algorithm is depicted in Figure 3.…”

“…Su et al [25] and Le et al [26] proposed implicit forcing methods solving implicit banded force matrix equations. In order to avoid the complicated calculation of the matrix equations, Luo et al [27] and Wang et al [19] proposed multi-direct-forcing, which iterates the procedure of forcing and spreading until a given criterion is satisfied, and applied it to fixed and moving particle problems.…”

“…For diffuse interface schemes, we consider the explicit diffuse interface scheme, as in [33], and the implicit diffuse scheme, as in [34]. The differences of this study from previous schemes [33,34] are: (i) to clearly see the effect of boundary diffuseness on accuracy, we adopt both 2-point and 4-point discrete delta functions, which give second-order approximations, whereas they [33,34] only used the cosine-type 4-point discrete delta function, which gives first-order approximation [36,37] and (ii) for the implicit diffuse interface scheme, we adopt the simple multi-direct-forcing scheme used under the IBM based on the NSE in [19,27] to avoid solving the complicated banded matrix equations as in [34]. For a sharp interface scheme, we consider the exterior sharp interface scheme used in the direct-forcing IBM based on the NSE by Kim et al [9], where forcing nodes are located on the exterior (solid) nodes.…”

Immersed boundary method for the simulation of 2D viscous flow based on vorticity–velocity formulations

“…In order to allow for a smooth transfer between Eulerian and Lagrangian representations while at the same time avoiding strong restrictions of the time step, Uhlmann [12] proposed an improved method to incorporate the regularized delta function approach into a direct formulation of the fluid-solid interaction force. Wang et al [13] and Luo et al [14] proposed an explicit multi-direct forcing approach based on the Peskin's original IB method [6] to obtain a better satisfaction of the no-slip boundary condition at the immersed boundary of rigid body than that of the original direct forcing approach. Feng and Michaelides [15] introduced a numerical method called Proteus combined the immersed boundary method, the direct forcing method and lattice Boltzmann method for the simulation of particulate flows.…”

Parallel computing strategy for the simulation of particulate flows with immersed boundary method

“…This technique has been applied to simulating the mutual interaction between stationary boundary and fluid flow [1,2,4,5,7] , and also to simulating the mutual interaction between oscillation boundary and fluid flow [4] . More recently, this technique has been used to simulate multiphase system [9,[11][12][13][14] .…”