Numerical simulation of particle motion using a combined MacCormack and immersed boundary method

A numerical approach is presented for the direct numerical simulation of particle motion that combines the MacCormack scheme and the immersed boundary method. It exhibits the advantageous features of the explicit MacCormack scheme which is second-order accurate in time and space with simplicity in programing. The approach solves the compressible Navier–Stokes equations and uses the immersed boundary method to tackle the interactions between the fluid and the suspended particles. The force due to the interaction of two phases is computed via an elastic forcing method. The numerical approach is validated using uniform flow past a stationary circular cylinder, sedimentation of circular discs, and particle motion (orientation and translation) in unidirectional flows. Results are also compared to simulation obtained from a mixture model for solid particles for the same flow conditions.