Analytical and Numerical Solutions to the Wave Diffraction Problems

Abstract

Wave interaction with rough bottom surfaces (topography), offshore drilling platforms and wave energy collectors is accompanied by the diffraction of waves. Here, an account is given of our research results in the field of wave diffraction. Specific aspects and methods used to solve the problems of the wave-diffraction theory are described in brief. The problem of wave diffraction by a submerged elliptical cylinder with elliptical lower face under an arbitrary incidence of plane waves is discussed. Wave diffraction by a submerged compound cylinder is also considered. Horizontal wave force is calculated as an example illustrating the dependence on the degree of submersion of the obstacle. Both the decrease of the submersion depth and the increase of the wave number are shown to favour the approach to the resonance range and thus worsen the reliability of the results. Scattering of magnetoacoustic waves by a cylinder is studied, the effect of magnetoelastic waves on the scattered field is demonstrated. Wave diffraction in a multiconnected domain formed by a set of vertical cylinders is analysed. The mutual influence of the cylinders is considerable for \( l/2a < 2 \), where l is the distance between the cylinders and 2a is the diameter. Interaction between diffracted fields is studied and the maximum lateral wave force that can also act outside the frontal cylinder is calculated. An exact analytical solution to the problem of wave diffraction by an asymmetrically inhomogeneous cylinder is found, the effect of asymmetry on the total scattering cross-section is analysed. An efficient numerical-analytical method is also considered, i.e. an auxiliary surface of simple shape (spherical or cylindrical) is introduced that surrounds the scatterer. In this case, the boundary-value problem can be subdivided into two problems, interior and exterior ones. The former is solved analytically in an infinite domain, the latter is solved numerically in a finite domain with a complex boundary. Furthermore, we study the wave diffraction by a prolate body of revolution consisting of a cylinder and spherical end cups. To solve the problem, a new finite-element algorithm is proposed.