A Sharp Interface Direct Forcing Immersed Boundary Approach for Fully Resolved Simulations of Particulate Flows

Abstract

In recent years, the immersed boundary method has been well received as an effective approach for the fully resolved simulations of particulate flows. Most immersed boundary approaches for numerical studies of particulate flows in the literature were based on various discrete delta functions for information transfer between the Lagrangian elements of an immersed object and the underlying Eulerian grid. These approaches have some inherent limitations that restrict their wider applications. In this paper, a sharp interface direct forcing immersed boundary approach based on the method proposed by Yang and Stern (Yang and Stern, 2012, “A Simple and Efficient Direct Forcing Immersed Boundary Framework for FluidStructure Interactions,â€‌ J. Comput. Phys., 231(15), pp. 5029–5061) is given for the fully resolved simulations of particulate flows. This method uses a discrete forcing approach and maintains a sharp profile of the fluidsolid interface. It is not limited to low Reynolds number flows and the immersed boundary discretization can be arbitrary or totally eliminated for particles with analytical shapes. In addition, it is not required to calculate the solid volume fraction in low density ratio problems. A strong coupling scheme is employed for the fluidsolid interaction without including the fluid solver in the predictorcorrector iterative loop. The overall algorithm is highly efficient and very attractive for simulating particulate flows with a wide range of density ratios on relatively coarse grids. Several cases are examined and the results are compared with reference data to demonstrate the simplicity and robustness of our method in particulate flow simulations. These cases include settling and buoyant particles and the interaction of two settling particles showing the kissingdraftingtumbling phenomenon. Systematic verification studies show that our method is of secondorder accuracy on very coarse grids and approaches fourthorder accuracy on finer grids.