A hybrid method for linearized wave radiation and diffraction problem by a three dimensional floating structure in a polynya

Abstract

A hybrid method is developed to solve the interaction problem of wave with a three dimensional floating structure in a polynya. The linearized velocity potential theory is used for fluid flow, and the thin elastic plate model is adopted for the infinitely extended ice sheet. Because of sudden change of the upper boundary of the computational domain, namely from the ice sheet to the free surface, the domain is divided into two sub-domains, one below free surface and the other below the ice sheet. The solution method is divided into three components. The first component is the integral equation over the structure surface and the interface of the two sub-domains. In the second component, the velocity potential is expanded into a series of eigenfunctions in the vertical directions, which avoids the numerical difficulty in calculation of the fifth derivatives. This is coupled with a series of integral equations along the edge of the ice sheet. In the third component of the method, two orthogonal inner products are used to impose the continuity conditions of the velocity and pressure on the interface, as well as the boundary conditions on the ice edge. The developed method is verified through comparison with the analytical solution for a circular cylinder. Case study is then made for a FPSO in a polynya with different shapes and floating positions. The hydrodynamic coefficients, wave exciting force and wave elevation in polynya are provided and analyzed.

Interactions of waves with a body floating in an open water channel confined by two semi-infinite ice sheets

“…Based on (A11) and (A14), we then have that the Green function G in (A4) is identical to that for free surface, or (Li et al 2020a)…”

“…As discussed following equation (3.55), the wave components of α j decay exponentially with respect to y. Thus, the leading term will be that due to the ring wave (Li et al 2020a), which is in the form of exp(−iκ 0 R)/ √ R with R = x 2 + y 2 . Using this, it can be seen that…”

“…Another reason is the fifth derivative on the ice sheet is not easy to compute numerically. Therefore, Li, Shi & Wu (2020a) developed a hybrid method for this problem, in which a series of integral equations under the ice sheet were constructed and coupled with the inner boundary integral equation through an orthogonal inner product. The solution procedure is highly efficient if the polynya is finite, and is effective even when there is more than one polynya or more than one structure.…”

Three-dimensional interaction between uniform current and a submerged horizontal cylinder in an ice-covered channel

“…When the ice sheet is not directly in contact with the surface of the structures, such as structures are located in a polynya or open water confined by ice sheets, mixed upper surface boundary conditions need to be considered. Ren, Wu & Ji (2018 b ) investigated wave diffraction and radiation by a vertical circular cylinder standing arbitrarily in a circular polynya, while Li, Shi & Wu (2020 a ) employed a hybrid numerical method and considered a floating structure of arbitrary shapes in a polynya with various shapes.…”

Numerical Simulation of a Polar Ship Moving in Level Ice Based on a One-Way Coupling Method

“…Experimental studies, including field tests [6][7][8] and model tests in ice tanks [9][10][11][12][13][14], are generally viewed as reliable; however, they are strict regarding the experimental facilities and methods used and are quite expensive so cannot be done easily. Analytical methods have a relatively long history from simple models to complex models [15][16][17][18][19][20]. However, they are usually based on many simplifications of body shape and ice model, which made them hard to extend to complex ship hulls and actual ice conditions.…”