| This thesis presents numerical methods for the simulation of free boundary and particulate flow problems arising in the field of biomechanics.;The essential part for solving these problems numerically is to have robust and efficient numerical methods for solving the Navier-Stokes equations, which are well-accepted models for the incompressible viscous Newtonian fluid flow. The simulations of the numerical solution of the Navier-Stokes equations has been carried out via methodology combining time discretization by a first order accurate operator-splitting, L2-projection and H1-projection Stokes solvers a la Uzawa and a wave-like equation treatment of the advection. The numerical results obtained for the classical wall-driven cavity flow problem show that both methodologies, which are fairly simple to implement, yield consistent results for Reynolds numbers (Re) up to 7500. This have reassured that the L2-projection method is an effective methodology.;The free boundary problem considered in this thesis is the blood flow in an artery with stenosis. The stenotic artery is modeled by an axisymmetric elastic tube with constriction subjected to a uniform external pressure and a prescribed pressure drop. The blood flow in such arteries is modeled by the Navier-Stokes equations and a nonlinear mathematical model for the free moving boundary. A distributed Lagrange multiplier-based fictitious domain (DLM/ND) method combined with operator splitting techniques and finite element method has been developed to simulate viscous incompressible flow in the above tube. The fictitious domain method developed in this work has shown its capability of investigating the fluid flow in a complex domain with a free moving boundary.;To study the red blood cell (RBC) rheology in microcirculation, an immersed boundary method coupled with a spring model, which describes the skeletal structure of the RBC membrane, has been developed. The biconcave RBC shape in static plasma and tank- treading behavior of single cell in simple shear flows have been successfully captured in this model. Shape behavior, lateral migration, and aggregation of the RBCs in microvessels have been investigated. The simulation results agree well with other people's experimental and numerical observations. |
