A simple and efficient parallel immersed boundary-lattice Boltzmann method for fully resolved simulations of incompressible settling suspensions

Abstract

This study presents an efficient and parallel fully resolved direct numerical simulation (FR-DNS) of settling suspensions on multiple CPU cores based on the boundary-thickening direct forcing immersed boundary method (BTDF-IBM) and incompressible lattice Boltzmann method (LBM). The simple BTDF-IBM is used to meet the no-slip and no-penetration conditions on particle boundaries, and the incompressible LBM is used to achieve the capability of large pressure fluctuations in suspensions. In addition, a theoretical force model is used to compensate for the unresolved lubrication force between the two approaching particles. A swap strategy for the streaming step is used to reduce the memory storage of the LBM particle density functions to half. A distribution and communication strategy is proposed to handle the IBM computing and complete the immersed boundary (IB) force of the particles residing in the interface region between adjacent subdomains. The developed BTDF-IBM-LBM solver “PFlows” can simulate large particle-laden flows with more than O(106) particles and with a particle volume fraction of up to 0.4. An almost linear parallel speedup and efficiency of higher than 0.8 are obtained by testing three-dimensional (3D) cases (up to 1.0 billion fluid grids and 0.45 million particles) and two-dimensional (2D) cases (up to 1.2 billion fluid grids and 2.39 million particles). Finally, the framework is applied to three large-scale real simulations involving 50,000 particles settling in 2D and 3D bounded and unbounded domains for qualitative and quantitative validations. The particle settling behaviors and disturbed complex fluid flows in the vertical channel are demonstrated. The Boycott effect in the inclined channel is uncovered by a new mechanism that combines particle sliding at the lower sidewall with fluid convection in the upper region. The hindered settling of particles in the 3D periodic domain, which is affected by the strong particle-fluid hydrodynamic interactions and particle-particle many-body interactions at a high solid volume fraction, are analyzed. The complex behaviors and statistical characteristics of the suspensions are preliminarily revealed and analyzed, which demonstrates the prospective capability of the present framework for FR-DNS of large-scale 2D and 3D suspension flows that are relevant to many industrial applications by IB-LBM.