An inverse problem in boundary-layer flows: Numerical determination of pressure gradient for a given wall shear

Abstract

The problem of determining a pressure gradient distribution that will produce a specified shear force on a body surface in boundary-layer flows is considered. This leads to an "overdetermined" boundary value problem for a partial differential equation containing an unknown coefficient. A numerical procedure for determining the coefficient is given along with several worked out examples including both similar and nonsimilar flows. The method essentially treats the unknown coefficient as an eigenvalue which is computed using Newton's method. This in turn employes a very accurate and efficient finite difference scheme for computing standard boundary-layer flows. Richardson extrapolation is applicable but only modest improvement was obtained in the present examples (for reasons that are explained).

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