An interface resolved immersed boundary method in XDEM for particulate flow simulations

immersed boundary method (IBM) has recently been used for particulate flows and complex fluid-solid interaction problems. The IBM was first introduced by Peskin to simulate blood flow in a beating heart. Later it has been extended for a different range of applications. The advantages of IBM over the body-fitted method is that it substantially simplified grid generation for immersed geometries, and it is easier to handle moving boundary situations. IBM even allows the use of a stationary and non-deformation background mesh, as well as it reduces the cost of computation by avoiding generation of a body-fitted mesh for each time step. However, the IBM approach is not straightforward to implement and it requires special techniques for cut-off boundary cells as well as special techniques for data point interpolations. Generally, the IBM is classified into two approaches based on the methods of imposing the boundary condition in the immersed body. The first approach is called fictitious domain method with continuous forcing scheme which employs a distributed forcing function to impose a rigidity boundary condition in the solid particle domain. The second one is the discrete forcing approach, which enables a sharp interface to represent the immersed surface. The IBM discussed in this work is a combination of these above two approaches: we first employ the continuous forcing scheme to get a first-step approximation of the immersed body, then use an interpolation polynomial to impose a desired accurate physical boundary for each immersed boundary point based on a least square interpolation reconstruction scheme.
Particle motions can be calculated and tracked by solving Newton’s equations of motions using the extended discrete element method (XDEM) while the data of fluid flow properties are obtained by solving the Navier-Stokes equations which govern the fluid phase. Combined this leads to the basic concept of DEM-CFD coupling. Therefore, a particle interface resolved simulation solver is developed by coupling the XDEM and IBM approaches together. Consequently, this solver is then used to handle both static and dynamic particle problems as well as particle packed bed simulations. The validation of the solver can be performed by setting one static sphere in a channel and evaluate the drag coefficients and Strouhal number (when shedding occurs) at various Reynolds