A numerical algorithm based on transformed partial differential equations for fluid flows.

Date of Award


Publication Type

Doctoral Thesis

Degree Name



Mechanical, Automotive, and Materials Engineering

First Advisor

Zhang, C.,


Engineering, Mechanical.




In the numerical simulation of fluid flows, difficulties arise from the non-linear convection terms which are expressed by the first-order spatial derivatives of the flow variables. Many attempts have been made to overcome this difficulty by using different differencing schemes to discretizing these terms. In this dissertation a new numerical method for solving partial differential equations is presented. The basic idea of this method is that the equations are first transformed by introducing an exponential function to eliminate the convection terms, then a fourth-order central differencing scheme and a second-order central differencing scheme are used to discretize the transformed equations. This method is first tested on partial differential equations that originate from the governing equations of the physical process of fluid flow. These partial differential equations include a model elliptic equation and a model parabolic equation. Results from the present method are compared against exact solutions and against results obtained by using four classical differencing schemes, namely, the first-order upwind scheme, hybrid scheme, power-law scheme, and exponential scheme. Next, this method is tested on fluid flows with exact solutions, which are self-designed quasi-fluid flow problems, the two-dimensional stagnation in plane flow (Hiemenz flow), and the flow between two concentric cylinders. Lastly, this method is used to simulate fluid flows without exact solutions, namely lid-driven cavity flow and flow over a backward-facing step. For the lid-driven cavity flow, the flow with v-velocity boundary condition is also studied. Benchmark solutions and experimental data are used for comparisons.Dept. of Mechanical, Automotive, and Materials Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2003 .X84. Source: Dissertation Abstracts International, Volume: 65-07, Section: B, page: 3676. Advisers: C. Zhang; R. Barron. Thesis (Ph.D.)--University of Windsor (Canada), 2004.

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