Fully nonlinear simulations of interactions between solitary waves and structures based on the finite element method

Fully nonlinear interactions between solitary waves and structures are studied based on a finite element method (FEM) in two-dimensions. A mesh with higher order 8-node quadrilateral isoperimetric element is used in the simulation. The velocity potential is obtained by solving a linear matrix system using the conjugate gradient (CG) method with a symmetric successive overelaxlation (SSOR) preconditioner, and the velocity in the fluid domain is calculated through differentiating shape functions directly. The wave elevation and potential on the free surface are updated by the fourth order Runge-Kutta method. Waves and hydrodynamic forces are obtained for single solitary waves acting on a wall and propagating on a tank with a step, collision between two solitary waves, interactions between a solitary wave and a single and twin rectangular cylinders on free surface. Some results are compared with previous studies of analytical solutions and those by experiment. The simulations have provided many results to show the nonlinearities of waves and hydrodynamic forces with different incoming wave amplitudes, and the effect of dimensions of the single cylinder and the spacing between twin cylinders on the wave and forces are also discussed.