The wave run-up is vertical up-rush of water around the partially immersed body on when incident wave impinges. In this present study, the wave run-up is investigated on fixed single or dual vertical cylinders in fully nonlinear waves. The VOF method based on two-step projection has been developed to Navier-Stokes equation and validated by the comparison with published results. Using the developed numerical codes, the nonlinear interaction between structures and waves are discussed. It is found that complicated interactions between diffracted waves generated by physical circumstances of the varying size of the cylinders and gap distances dominate the complete wave run-up around structures.
Investigation of the wave interactions on and around the large columns is very important in the design of the coastal structures, since the precise calculation and prediction of the physical phenomena can provide sufficient information for safe and economic design. MacCamy and Fuchs (1954) first developed a linear diffraction theory in finite depth water for calculating the wave forces on a vertical bottom mounted and fixed cylinder. However, evidences from experiments that the nature of water waves is, in general, inherently nonlinear and unsteady has been found through a variety study by many researchers. Numerical modeling of nonlinear wave diffraction around large offshore structures are needs to obtain more accurate wave force and run-up predications than those of linear diffraction theory which is based on the assumption of infinitesimal wave heights. The wave nonlinear problem is much more difficult to study in analytical form. For last decades, considerable efforts have been devoted to the analytical solution of the second order wave diffraction for single or multi-arrayed cylinders. A second order frequency domain solution based on the Stokes perturbation procedure (Molin, 1979, Kioka and Ishida, 1984, Eatock Tayor etc., 1989) has been developed to solve the wave diffraction around the fixed vertical circular cylinder.
