Two new concepts have been explored in solving the neutron
diffusion equation in one and two dimensions. At the present time,
the diffusion equation is solved using source iterations. These
iterations are performed in a mathematical form which has a great
deal of physical significance. Specifically, the neutron production
term...
This dissertation explores mathematical theory of the 3 dimensional incompressible Navier-Stokes equations that consists a set of partial differential equations which govern the motion of Newtonian fluids and can be seen as Newton's second law of motion for fluids. The main interest of this work focuses on how local perturbation...
In this thesis some methods for solving systems of
nonlinear equations are described, which do not require
calculation of the Jacobian matrix. One of these methods
is programmed to solve a parametrized system with possible
singularities. The efficiency of this method and a modified
Newton's method are compared using experimental...
A nonlinear wave equation is developed, modeling the evolution in time of shallow water waves over a variable topography. As the usual assumptions of a perfect fluid and an irrotational flow are not made, the resulting model equation is dissipative due to the presence of a viscous boundary layer at...
In this work, flow through synthetic arrangements of contacting spheres is studied
as a model problem for porous media and packed bed type flows. Direct numerical
simulations are performed for moderate pore Reynolds numbers in the range,
10 ≤ Re ≤ 600, where non-linear porescale flow features are known to...