Date of Award
Mathematics and Statistics
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This thesis studies steady, two dimensional flow of an inviscid, incompressible fluid over an arbitrary symmetric profile. Flows with zero and variable vorticity are considered. In the present work a numerical algorithm is given for a class of lows that can also be solved by perturbation techniques. However, reliable solutions by the perturbation technique, especially in the case of rotational flows, require complicated analytical methods even in the case of the circle. Thus, one of the goals of this thesis is to provide a fast and efficient algorithm from which a solution to several standard problems can be obtained with less effort. The equations of motion based on a transformation of coordinate systems are derived. The approach is new in that the computational domain consists of the streamlines (psi)(x,y) = constant and an arbitrary family of curves (phi)(x,y) = constant such that the ((phi),(psi)) coordinate system forms a curvilinear net. To solve the flow the transformed equations are simplified based on the flow assumptions. Boundary conditions of the mixed type are then applied to the computational domain. Results are presented for several aerodynamic profiles and compared with those obtained by other methods. The proposed method is found to be fast, efficient and reliable. Accurate results can be obtained with a minimum of numerical calculation. A stability analysis of the ADI (Alternating-Direction-Implicit) iteration method is carried out, based on a Fourier series method. A new equation for the error is obtained. It is found possible to obtain a precise interval where convergence is optimized for a certain class of elliptic partial differential equations.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1986 .G767. Source: Dissertation Abstracts International, Volume: 47-05, Section: B, page: 2016. Thesis (Ph.D.)--University of Windsor (Canada), 1986.
GROSSMAN, GEORGE WILLIAM., "FINITE-DIFFERENCE ALGORITHMS FOR INVISCID, INCOMPRESSIBLE FLOW OVER AN ARBITRARY SYMMETRIC PROFILE." (1986). Electronic Theses and Dissertations. 2112.