Integral equation techniques for wave-structure interaction problems

Abstract:  Integral equation techniques are very much useful for solving a number of real engineering problems arise in the broad area of hydrodynamics. Due to the presence of higher order boundary conditions in the BVP, often usual analytic/semi-analytic solution techniques are not applicable and for the same, integral equation techniques are often used for solution purpose. In this talk, three different solution techniques based on integral equations will be discussed. In the first problem, using free space Green’s function, the boundary value problem is converted into a system of Fredholm integral equations (second kind) which are solved using Boundary Element Method. Further, for better accuracy and efficiency, the aforementioned tool is coupled with the eigenfunction expansion method. In the second problem, the associated BVP is converted into a system of Fredholm integral equations of second kind using free surface Green’s function and finally converted into a system of equations and solved using suitable quadrature formulae. Using Green’s second identity, energy balance relations are derived and used to check the accuracy of the numerical results. In the third problem, the associated BVP is solved using two different approaches. In the first approach, the aforementioned Fredholm integral equation technique is used and for the second approach, the BVP is converted into an integro-differential equation and finally solved by constructing appropriate eigenfunctions. The numerical convergence of the solutions are also discussed. One of the major advantage of these aforementioned techniques is that these techniques can handle arbitrary shape of the boundaries and higher order boundary conditions.