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Hilbert's method for numerical solution of flow from a uniform chennel over a shelf

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Summary

A nonlinear problem for the flow from a uniform channel over a shelf has been solved, using conformal mapping and the Hilbert solution of a mixed-boundary-value problem in the upper half-plane. The solution in the gravity-affected case was found by numerical iteration; the nongravity solution was used as an initial approximation. The numerical solutions obtained have been compared with those of other authors. Favourable agreement with the results of experiments suggest that this method is effective in dealing with flow problems strongly influenced by gravity. Some difficulties of the computing, and some checking of the solution, are discussed.

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Author notes

  1. M. B. Abd-El-Malek

    Present address: Department of Mathematics and Physics, Faculty of Engineering, Alexandria University, Alexandria, Egypt

Authors and Affiliations

  1. Department of Mathematics, University of Windsor, N9B 3P4, Windsor, Ontario, Canada

    A. C. Smith & M. B. Abd-El-Malek

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  1. A. C. Smith
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  2. M. B. Abd-El-Malek
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Smith, A.C., Abd-El-Malek, M.B. Hilbert's method for numerical solution of flow from a uniform chennel over a shelf. J Eng Math 17, 27–39 (1983). https://doi.org/10.1007/BF00042836

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  • DOI: https://doi.org/10.1007/BF00042836

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