Numerical solution of free surface flow problem
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Date
2024
Journal Title
Journal ISSN
Volume Title
Publisher
Mohamed Boudiaf University in Msila
Abstract
An approximate method is presented to solve the problem of steady free-surface flow of
an ideal fluid over a semi-infinite ramp in the bottom. Schwartz-Christoffel transformation
is used to map the region of flow, in the complex potential-plane, onto the upper halfplane. The Hilbert transformation as well as the perturbation technique are used as a basis
for the approximate solution of the problem for large Froude number and small inclination
angle of the ramp. General equations, in integral form, for any order of approximation
are obtained. Solution up to first-order approximation is discussed and illustrated.
Description
Keywords
Free-surface flow problems, Schwartz-Christoffel transformation, Hilbert transformation, perturbation technique, nonlinear integral equations