Maximum principle preserving high order schemes for convection-dominated diffusion equations

The maximum principle is an important property of solutions to PDE. Correspondingly, it's of great interest for people to design a high order numerical scheme solving PDE with this property maintained. In this thesis, our particular interest is solving convection-dominated diffusion equation. We first review a nonconventional maximum principle preserving(MPP) high order finite volume(FV) WENO scheme, and then propose a new parametrized MPP high order finite difference(FD) WENO framework, which is generalized from the one solving hyperbolic conservation laws. A formal analysis is presented to show that a third order finite difference scheme with this parametrized MPP flux limiters maintains the third order accuracy without extra CFL constraint when the low order monotone flux is chosen appropriately. Numerical tests in both one and two dimensional cases are performed on the simulation of the incompressible Navier-Stokes equations in vorticity stream-function formulation and several other problems to show the effectiveness of the proposed method.

Preserving and interpreting the mining company office : landscape, space and technological change in the management of the copper industry

The purpose of this research is to examine the role of the mining company office in the management of the copper industry in Michigan’s Keweenaw Peninsula between 1901 and 1946. Two of the largest and most influential companies were examined – the Calumet & Hecla Mining Company and the Quincy Mining Company. Both companies operated for more than forty years under general managers who were arguably the most influential people in the management of each company. James MacNaughton, general manager at Calumet and Hecla, worked from 1901 through 1941; Charles Lawton, general manager at Quincy Mining Company, worked from 1905 through 1946. In this case, both of these managers were college-educated engineers and adopted scientific management techniques to operate their respective companies. This research focused on two main goals. The first goal of this project was to address the managerial changes in Michigan’s copper mining offices of the early twentieth century. This included the work of MacNaughton and Lawton, along with analysis of the office structures themselves and what changes occurred through time. The second goal of the project was to create a prototype virtual exhibit for use at the Quincy Mining Company office. A virtual exhibit will allow visitors the opportunity to visit the office virtually, experiencing the office as an office worker would have in the early twentieth century. To meet both goals, this project used various research materials, including archival sources, oral histories, and material culture to recreate the history of mining company management in the Copper Country.