We discuss a mathematical model arising from the following
physical situation. We consider a gas-filled cylinder with a piston
at one end whose motion is determined by the pressure of the gas
within the cylinder and by external forces. Zero mass flux is
assumed at the piston while the mass...
The study of water movement in unsaturated soils by using appropriate
diffusion equations has attracted considerable attention in
recent years.
In this study, a numerical technique is developed for solving
a generalized, dimensionless diffusion equation by the use of a digital.
computer. Diffusivity and capillary conductivity equations derived
by Brooks...
This thesis introduces a technique for approximating to a desired
degree of accuracy a linear parabolic equation of two spatial
dimensions with given initial data and prescribed boundary conditions.
The technique is generalized to non-linear parabolic equations.
It is stable for all mesh ratios, and it is second order accurate...
This thesis examines various net or finite difference methods
for solving parabolic partial differential equations in one space variable
with constant coefficients. Included in this investigation are
explicit, implicit and multi-step methods of varying orders of accuracy.
These methods are compared with respect to accuracy, speed,
efficiency, stability, simplicity of...
In this thesis, problems arising in pumping fluids
from the ground are treated. The mathematical theory is
derived for both the time dependent and independent cases.
A numerical method is developed to solve these problems.
Some particular examples are presented and computer plots
are drawn to illustrate the movement of...
Because of competition from abroad, the U. S. Steel
industry has begun research into the processes involved
with electric arc steelmaking. This paper addresses the
mathematical background of these furnaces and the electro-magneto-
hydrodynamical effects used to melt the large
quantities of steel. A classical approach to the
derivation of...
An analysis was conducted to determine the effects of nonlinearity in
the one dimensional Navier-Stokes equation describing a viscous fluid flow.
An attempt was made to numerically determine the effect of temperature
variance on the fluid, either by varying the constant viscosity factor in the
energy dissipative term in the...
The two dimensional wavemaker problem on a finite domain is derived
for nonlinear waves. A numerical method based on the method of lines is
developed and applied to two test problems, the nonlinear surface pressure
distribution problem and the nonlinear full-flap wavemaker problem. The
solutions yield information about the fluid...
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...
