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A Finite Element-Differential Methof for incompressible Turbulent Boundary-Layer Flows

Report Number: AFWAL TR 81-3174
Author(s): Tyne-Hsien Chang; Chen-Chi Hsu
Corporate Author: University of Florida Department of Engineering Sciences
Date of Publication: 1982-02-01
Pages: 78
AD Number: ADA112821

Abstract:
The applicability as well as the accuracy and efficiency of a finite element-differential method, which had been shown to be a very effective method for laminar flows, is investigated in detail for more complex steady two-dimensional incompressible turbulent boundary layer flow problems. The closure model chosen for the turbulent flows is a two-layer eddy viscosity model. A number of important transformations have been carried out for the system of governing equations before the application of the proposed solution method. In the method of solution, the transformed partial differential equation is first reduced to a system of first order nonlinear ordinary differential equations by a subdomain collocation method, in which the unknown function at a streamwise station is represented by a classical spline function. The resulting initial value problem is then integrated numerically by the modified Hamming's predictor-corrector method as well as by Gear's method for stiff equations. The numerical experiments have been conducted on the flat plate problem which consists of the laminar, transitional, and turbulent flow regions covering the range of local Reynolds numbers from 800 to 800 million. The study shows that the method of solution can be very efficient and provides highly accurate results for the turbulent flow problem.

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