The present work is a study of three degenerate, linear parabolic
systems of equations, each of which represents a version of the so-called
double porosity model for underground fluid flows in natural fractured
rock. These systems of equations together with initial and boundary
conditions describe single-phase flows in fluids, slightly...
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...
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...