Analytical Solution for Froude–Krylov Force of Triangulated Geometry in Linear Waves

Abstract

For wave exciting load on offshore structures, Froude–Kyrlov (FK) force is easier to evaluate than diffracting force. But current nonlinear FK models suffer low computational speed. Conventionally, FK force is calculated by performing Gaussian quadrature (GQ) on each surface mesh, and the choice of the mesh size is important in order to resolve wave characteristics both in the propagation and depth directions. Therefore, either by limiting the size of a surface mesh under one-tenth of the wavelength or increasing the order of GQ, numerical errors can be minimized. For the purpose of relieving the above restriction, the analytical integration of the dynamic pressure field in the time domain over a triangular mesh is derived to avoid the mesh-dependent errors and to improve computational efficiency. It will be shown that the solution of integration obtained in time domain can be cast in the frequency domain under linearized free surface conditions. Validation includes the analytical solution to a cuboid at head sea and numerical solutions to a catamaran by commercial software. The results show excellent agreement for general wave conditions and prominence at very high-frequency range. In terms of computational efficiency, we compared the execution time against GQ with different orders and showed the analytical method is significantly faster. The limitation of this method is in very long waves or for degenerated panels, which are specifically addressed by line integration.