A boundary thickening-based direct forcing immersed boundary method for fully resolved simulation of particle-laden flows

Abstract

A boundary thickening-based direct forcing (BTDF) immersed boundary (IB) method is proposed for fully resolved simulation of incompressible viscous flows laden with finite size particles. By slightly thickening the boundary thickness, the local communications between the Lagrangian points on the solid boundary and their neighboring fluid Eulerian grids are improved, based on an implicit direct forcing (IDF) approach and a partition-of-unity condition for the regularized delta function. This strategy yields a simple, yet much better imposition of the non-slip and non-penetration boundary conditions than the conventional direct forcing (DF) technique. In particular, the present BTDF method can achieve a numerical accuracy comparable with other representative improved methods, such as multi-direct forcing (MDF), implicit velocity correction (IVC) and the reproducing kernel particle method (RKPM), while its computing cost remains much lower than them and nearly equivalent to the conventional DF method. The dependence of the optimum thickness value of boundary thickening on the form of the different regularized delta functions is also revealed. By coupling the lattice Boltzmann method (LBM) with BTDF-IB, the robustness of the present BTDF IB method is demonstrated using numerical simulations of creeping flow (Re=0.1), steady vortex separating flow (Re=40) and unsteady vortex shedding flow (Re=200) around a circular cylinder. The accuracy and robustness of the present method for moving particle-laden flows are performed on three benchmark cases, such as free sedimentation of single circular cylinder, DKT sedimentation of two particles and Rayleigh-Taylor instability of 504 particles sedimentation in an enclosed cavity. The computational efficiency between the present BTDF method and the MDF method is also compared at last.