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Numerical simulation of particle motion using a combined MacCormack and immersed boundary method. (English) Zbl 1349.76560

Summary: 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.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M75 Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76Nxx Compressible fluids and gas dynamics
76T20 Suspensions
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