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Use of Galerkin Technique in Some Water Wave Scattering Problems Involving Plane Vertical Barriers

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Applied Mathematical Analysis: Theory, Methods, and Applications

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 177))

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Abstract

The explicit solutions exist for normal incidence of the surface wave train or a single thin plane vertical barrier partially immersed or completely submerged in deep water. However, for oblique incidence of the wave train and/or for finite depth water, no such explicit solution is possible to obtain. Some approximate mathematical techniques are generally employed to solve them approximately in the sense that quantities of physical interest associated with each problem, namely the reflection and transmission coefficients, can be obtained approximately either analytically or numerically. The method of Galerkin approximations has been widely used to investigate such water wave scattering problems involving thin vertical barriers. Use of Galerkin method with basis functions involving somewhat complicated functions in solving these problems has been carried out in the literature. Choice of basis functions as simple polynomials multiplied by appropriate weights dictated by the edge conditions at the submerged end points of the barrier providing fairly good numerical estimates for the reflection and transmission coefficients have been demonstrated in this article.

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Authors and Affiliations

  1. Physics and Applied Mathematics Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata, 700 108, India

    B. N. Mandal

  2. Department of Applied Mathematics, University of Calcutta, 92, A.P.C. Road, Kolkata, 700 009, India

    Soumen De

Authors
  1. B. N. Mandal
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  2. Soumen De
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Correspondence to B. N. Mandal .

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Editors and Affiliations

  1. Department of Mathematics, Gauhati University, Guwahati, India

    Hemen Dutta

  2. Computational Intelligence Laboratory, Department of Electrical & Computer Engineering, University of Manitoba, Winnipeg, MB, Canada

    James F. Peters

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Mandal, B.N., De, S. (2020). Use of Galerkin Technique in Some Water Wave Scattering Problems Involving Plane Vertical Barriers. In: Dutta, H., Peters, J. (eds) Applied Mathematical Analysis: Theory, Methods, and Applications. Studies in Systems, Decision and Control, vol 177. Springer, Cham. https://doi.org/10.1007/978-3-319-99918-0_13

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