Combined multi-direct forcing and immersed boundary method for simulating flows with moving particles

Accurate description of particle–fluid interaction is one of the big challenges in the community of multiphase flows. Toward this direction, the combined multi-direct forcing and immersed boundary method were presented to simulate flows laden with finite-size moving particles with full-scale solutions. In the approach, the hydrodynamic interactions between moving rigid boundary and fluid were calculated using the multi-direct forcing scheme. The no-slip boundary conditions at the immersed boundaries can be satisfied well in this way. Direct numerical simulations of particle sedimentation under various conditions were performed based on the multi-direct forcing scheme, the immersed boundary method and the high-order finite difference. It is proved that this approach can successfully simulate the interactions between fluid and particle, the interactions between particle and particle as well as the interactions between particles and wall. The hitting and rebounding process of the single particle sedimentation, the drafting–kissing–tumbling of two settling particles and many particles sedimentation were observed. The quantitative comparisons against other studies were also conducted to validate the present approach.