Numerical methods and simulations for fluid /particle interactions: Sedimentation in a viscoelastic fluid and cell lifting in shear flow

In this dissertation I have considered the two-dimensional particulate flows problems in both Newtonian and viscoelastic fluids.;For the problem of cell adhesion to and detachment from surface in shear flow, cells are treated as neutrally buoyant rigid particles, and the fluid is a Newtonian incompressible viscous fluid modeled by the Navier-Stokes equations. I use Adhesive Dynamics ([30]) to model cell adhesion to surface. The fluid-cell system is solved by a distributed Lagrange multiplier/fictitious domain method for neutrally buoyant circular cylinders developed in [61]. Numerical simulations of processes of detachments of cells from surface under different flow conditions have been presented. Numerical simulation for the case with deterministic adhesion has also been presented. The simulated detachment percentages qualitatively agree with those from experiment.;Compared to Newtonian fluids, viscoelastic fluids are much more complicated. Developing numerical methods for viscoelastic fluids and particulate flows in viscoelastic fluids is quite challenging. The flow problem in a viscoelastic fluid is sedimentation of circular particles in a vertical channel filled with an Oldroyd-B fluid. I have developed a novel distributed Lagrange multiplier/fictitious domain method (DLM) for the numerical simulation of the problem. This method is based on the original algorithm for the Newtonian case by Glowinski et al. in [25]. In deriving the scheme, I have utilized an operator-splitting technique to decouple the difficulties associated with incompressibility, advection, and rigid body motion enforcement, in combination with factorizing the configuration tensor, which is the technique used by Lozinski and Owens in [59]. The new scheme preserves the positive definiteness of the configuration tensor at discrete levels of time. Numerical simulations of sedimentations of one circular particle, two particles side by side, and several particles in an Oldroyd-B fluid have been presented. The results agree well with those in the literature and experimental observations.