Boundary Condition Methods In The Numerical Solution Of The Navier-stokes Equations With The Application To Free Surface Problems

This thesis is divided into two main parts. Each is related to the numerical simulation of fluid flows. The first part is concerned with the treatment of pressure or vorticity boundary conditions in the numerical solution of the Navier-Stokes equations; and the second part is concerned with the numerical algorithm for simulating the dynamics of capillary surface.;In Part I, two new accurate finite-difference algorithms are described. They can be easily adapted on a uniform grid for solving general flows. The first approach, designated as Zero Perturbation Method, uses the combination of the momentum and divergence equations at the boundary to provide the implicit pressure boundary conditions. The second approach, designated as Computational Boundary Condition Method, utilizes a computational solution domain to avoid the problems of no explicit boundary conditions for pressure or vorticity in the Navier-Stokes equations.;Numerical experiments were carried out by second-order finite difference approach and alternating direction implicit (ADI) solution procedure. All tests were performed on uniform grids by means of Zero Perturbation Method and Computational Boundary Condition Method. The computed convergence rates for all variables are in excellent agreement with the theoretical prediction. Results for the classical driven cavity problem are found to be very accurate in comparison to previous investigators.;In Part II, the analysis has been made on the dynamics of liquids in a low gravity environment which is essentially dominated by its capillary effects. There are two major difficulties in numerical simulation: (i) accurate tracking of the curvature of an interface undergoing large deformations; (ii) diagnosing the initiation break-up of an interface, i.e. break-up of a liquid drop. A successful resolution of these difficulties requires an algorithm capable of accurate determination of pressure and velocities along the deformed interface. The required algorithms are described in Part II