scispace - formally typeset
Search or ask a question
Author

B. C. Das

Bio: B. C. Das is an academic researcher from University of Calcutta. The author has contributed to research in topics: Galerkin method & Scattering. The author has an hindex of 2, co-authored 5 publications receiving 11 citations.

Papers
More filters
Journal ArticleDOI
TL;DR: In this paper, a two-term Galerkin approximation involving simple polynomials as basis multiplied by appropriate weight function is used to solve the integral equations arising in the mathematical analysis of the oblique scattering problem.
Abstract: This paper is concerned with scattering of obliquely incident surface waves by a thin vertical barrier which may be either partially immersed or completely submerged extending infinitely downwards in deep water. Instead of one-term Galerkin approximation involving the known solution of the integral equation arising in the normal incidence problem, two-term Galerkin approximation involving simple polynomials as basis multiplied by appropriate weight function is used to solve the integral equations arising in the mathematical analysis of the oblique scattering problem. Very accurate numerical estimates for the reflection coefficient for each configuration of the barrier are obtained. The reflection coefficient is depicted graphically against the wavenumber and the incident angle for each configuration.

6 citations

Journal ArticleDOI
TL;DR: In this paper, the problem of oblique scattering of surface waves by a partially immersed rectangular barrier or a thick submerged rectangular barrier extending infinitely downwards in deep water is studied to obtain the reflection and transmission coefficients semi-analytically.
Abstract: The problem of oblique scattering of surface waves by a thick partially immersed rectangular barrier or a thick submerged rectangular barrier extending infinitely downwards in deep water is studied here to obtain the reflection and transmission coefficients semi-analytically. Use of Havelock’s expansion of water wave potential function reduces each problem to an integral equation of first kind on the horizontal component of velocity across the gap above or below the barrier. Multi-term Galerkin approximations involving polynomials as basis functions multiplied by appropriate weight functions are used to solve these equations numerically. Evaluated numerical results for the reflection coefficients are plotted graphically for both the barriers. The study reveals that the reflection coefficient depends significantly on the thickness of the barrier. The accuracy of the numerical results is checked by using energy identity and by obtaining results available in the literature as special cases.

3 citations

Book ChapterDOI
09 Jan 2018
TL;DR: In this paper, the problem of oblique scattering by fixed thin vertical plate submerged in deep water is studied by employing single-term Galerkin approximation involving constant as basis multiplied by appropriate weight function after reducing it to solving a pair of first kind integral equations.
Abstract: The problem of oblique scattering by fixed thin vertical plate submerged in deep water is studied here, assuming linear theory, by employing single-term Galerkin approximation involving constant as basis multiplied by appropriate weight function after reducing it to solving a pair of first kind integral equations. Upper and lower bounds of reflection and transmission coefficients when evaluated numerically are seen to be very close so that their averages produce fairly accurate numerical estimates for these coefficients. Numerical estimates for the reflection coefficient are depicted graphically against the wave number for different values of various parameters. The numerical results obtained by the present method are found to be in an excellent agreement with the known results.

3 citations

Journal ArticleDOI
01 Dec 2019
TL;DR: In this paper, the problem of oblique scattering of surface water waves by a vertical wall with a gap submerged in infinitely deep water is re-investigated in terms of two first kind integral equations, one involving the difference of potential across the wetted part of the wall and the other involving the horizontal component of velocity across the gap.
Abstract: The problem of oblique scattering of surface water waves by a vertical wall with a gap submerged in infinitely deep water is re-investigated in this paper. It is formulated in terms of two first kind integral equations, one involving the difference of potential across the wetted part of the wall and the other involving the horizontal component of velocity across the gap. The integral equations are solved approximately using one-term Galerkin approximations involving constants multiplied by appropriate weight functions whose forms are dictated by the physics of the problem. This is in contrast with somewhat complicated but known solutions of corresponding deep water integral equations for the case of normal incidence, used earlier in the literature as one-term Galerkin approximation. Ultimately this leads to very closed (numerically) upper and lower bounds of the reflection and transmission coefficients so that their averages produce fairly accurate numerical estimates for these coefficients. Known numerical results for normal incidence and for a narrow gap obtained by other methods in the literature are recovered, thereby confirming the correctness of the method employed here.

2 citations


Cited by
More filters
01 Jan 2016
TL;DR: The table of integrals series and products is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can get it instantly.
Abstract: Thank you very much for downloading table of integrals series and products. Maybe you have knowledge that, people have look hundreds times for their chosen books like this table of integrals series and products, but end up in harmful downloads. Rather than reading a good book with a cup of coffee in the afternoon, instead they cope with some harmful virus inside their laptop. table of integrals series and products is available in our book collection an online access to it is set as public so you can get it instantly. Our book servers saves in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Merely said, the table of integrals series and products is universally compatible with any devices to read.

4,085 citations

Journal ArticleDOI
TL;DR: In this paper, an analysis for the propagation of oblique water waves passing through an asymmetric submarine trench in presence of surface tension at the free surface is presented, where reflection and transmission coefficients are evaluated applying appropriate multi-term Galerkin approximation technique in which the basis functions are chosen in terms of Gegenbauer polynomial of order 1 / 6 with suitable weights.

12 citations

Journal ArticleDOI
TL;DR: In this paper, the problem of oblique scattering of surface waves by a partially immersed rectangular barrier or a thick submerged rectangular barrier extending infinitely downwards in deep water is studied to obtain the reflection and transmission coefficients semi-analytically.
Abstract: The problem of oblique scattering of surface waves by a thick partially immersed rectangular barrier or a thick submerged rectangular barrier extending infinitely downwards in deep water is studied here to obtain the reflection and transmission coefficients semi-analytically. Use of Havelock’s expansion of water wave potential function reduces each problem to an integral equation of first kind on the horizontal component of velocity across the gap above or below the barrier. Multi-term Galerkin approximations involving polynomials as basis functions multiplied by appropriate weight functions are used to solve these equations numerically. Evaluated numerical results for the reflection coefficients are plotted graphically for both the barriers. The study reveals that the reflection coefficient depends significantly on the thickness of the barrier. The accuracy of the numerical results is checked by using energy identity and by obtaining results available in the literature as special cases.

3 citations

Journal ArticleDOI
TL;DR: In this article, the mixed boundary value problem associated with scattering of obliquely incident water waves by a flexible porous barrier of different barrier configurations is considered and a novel connection is established between the solution potential of the converted problem and a resolvable potential in the quarter-plane.

2 citations

Journal ArticleDOI
TL;DR: In this article, an integral equation method was developed to study the wave interaction with two symmetric permeable plates submerged in a two-layer fluid, where the plates are inclined and penetrate the common interface between the layers.
Abstract: An integral equation method is developed to study the wave interaction with two symmetric permeable plates submerged in a two-layer fluid. The plates are inclined and penetrate the common interface between the layers. The existence of two different wave modes for the incident wave gives rise to two problems. Both of these are tackled by reducing them to a set of coupled hypersingular integral equations of the second kind. Unknown functions of the integral equations are the discontinuities in the potential functions across portions of the plates. These are computed numerically by employing an expansion collocation method. New results for the reflection coefficients and the amount of energy loss are presented by varying several parameters such as porosity, angle of inclination, plate-length, separation between the plates, interface position and density ratio. Known results for two symmetric vertical permeable and impermeable plates, single vertical impermeable and horizontal permeable plates are recovered from the present analysis.

2 citations