A modified immersed boundary method for simulations of fluid–particle interactions

According to the velocity distribution characteristics at the boundary layer of the solid body when the flow Reynolds number Rep = 0 and Rep → ∞, a nonlinear-weighted average scheme is proposed to fully-resolved direct numerical simulation of fluid–particle interactions combined with the ideas of immersed boundary method (IB method) and direct-forcing. The computational nodes near the solid boundary are divided into five categories, and different schemes are applied to them to impose the non-slip boundary conditions on the nodes inside the immersed body and to set a proper velocity distribution on the nodes outside the immersed body. Calculating the hydrodynamic force in this way can avoid the large gradient of density at the immersed boundary and can efficiently simulate fluid–particle interactions with full-scale solutions. To validate the computational strategy and its accuracy, the flow past a fixed spherical particle and the sedimentation of one and two particles are simulated based on high-order finite difference and parallel computing. The numerical results agree well with related experimental data, which show that the present method can be used to efficiently simulate the fluid–particle interactions.