http://hdl.handle.net/1957/16491 2013-05-23T16:01:01Z http://hdl.handle.net/1957/38394 Time dependent wavemaker problem for linear waves Cooper, Julia M. The classical two-dimensional wavemaker problem is formulated for linear waves. Two conformal mappings are applied to the mathematical formulation to transform the wavemaker problem into a unit disk. It is then shown that this technique cannot produce in practice a numerical representation of the fluid motion throughout time for any position in the wavemaker channel. An analytic solution to the classical wavemaker problem is developed and then solved numerically. This solution contibutes information about the fluid motion for all time and for any position in the wavemaker channel. In addition to this problem, a related initial value problem is solved theoretically and then numerically. This results in the surface wave and fluid motion being described for all time and all positions in a two dimensional, semi-infinite channel. Graduation date: 1990 1989-05-18T00:00:00Z http://hdl.handle.net/1957/38095 A heterogeneous flow numerical model based on domain decomposition methods Zhang, Yi In this study, a heterogeneous flow model is proposed based on a non-overlapping domain decomposition method. The model combines potential flow and incompressible viscous flow. Both flow domains contain a free surface boundary. The heterogeneous domain decomposition method is formulated following the Dirichlet-Neumann method. Both an implicit scheme and an explicit scheme are proposed. The algebraic form of the implicit scheme is of the same form of the Dirichlet--Neumann method, whereas the explicit scheme can be interpreted as the classical staggered scheme using the splitting of the Dirichlet-Neumann method. The explicit scheme is implemented based on two numerical solvers, a Boundary element method (BEM) solver for the potential flow model, and a finite element method (FEM) solver for the Navier-Stokes equations (NSE). The implementation based on the two solvers is validated using numerical examples. Graduation date: 2013 2013-03-14T00:00:00Z http://hdl.handle.net/1957/37971 Real algebraic geometry and the Pierce-Birkhoff conjecture Klute, Annette Graduation date: 1991 1991-03-28T00:00:00Z http://hdl.handle.net/1957/37721 A computer subroutine for the numerical solution of nonlinear Fredholm equations Tieman, Henry William Graduation date: 1991 1991-04-25T00:00:00Z