Research And Application Of Numerical Model On Waves Action With Obstacles

Based on review of various numerical wave models, research on vertical 2D and 3D numerical wave models are performed, aiming at the development and application of the numerical model in the aspects of analysis of the interaction between waves and obstacles. The dynamic characteristics of wave action on vertical seawall, quarter- circular breakwater and semi-circle breakwater are studied by using the vertical 2D numerical wave model under both submerged and emerged conditions. A 3D numerical wave model is presented based on the 3D N-S equations, in which the level set approach is used for free surface tracking. Comparing with plane propagation wave models, numerical models for wave action on obstacles are difficult and relatively less advanced. Since such kind of numerical model describes the instantaneous process of wave action and can give details of the current field, which is far more outstanding than the physical model and other traditional analyzing methods, it is thus of great importance to develop a numerical model of wave action on obstacles and to use it.The free surface tracking method is the key technique in developing the vertical 2D and 3D numerical wave models. Consequently, we at first carried out some research on this topic. Among the free surface tracking methods, the level set method is simple in terms of coding and describing the free surface combination, crossing and breaking. In order to apply it to the 3D numerical wave model, we verified this method in a shifting, rotating and shearing current field, respectively. The results show that this method can not model surface without distortion when large surface curvature is simulated, while particle level set method can mend this problem.The governing equations of the vertical 2D model are the Reynolds-averaged Navier-Stokes equations for incompressible viscous fluid. The Reynolds stress terms are closed by the k ?εturbulence transportation model. It can simulate small amplitude wave, Stokes wave, cnoidal wave, solitary wave and irregular wave acting on obstacles by source function wave generating method. It can also simulate wave-current motion inside porous structure such as rubble mound foundation. The main advantage of this model is its consideration for nonlinearity, viscosity and turbulence effect. The two-step projection method is used to solve the equations. Comparison of the modeled results with laboratory measurements in the case of wave action with vertical seawall and quarter-circular breakwater show good consistency interms of wave profiles, wave pressure, wave force, reflection and pattern of current field.The flow fields are investigated under submerged and emerged conditions by the vertical 2D numerical wave model for the cases of vertical seawall, quarter-circular type breakwater and semi-circle type breakwater. New findings are as follows. (1) When the vertical seawall is submerged, vertical vortex generally occurs and the closer the top of the vertical seawall to the still water level, the stronger the vortex is, which can be not obtained by potential theory or empirical formula. The bottom maximum current velocity occurs when the top of the vertical seawall is around the still water level. The numerical results indicate that under standing wave condition the empirical formula for wave pressure such as the Sainflou's, cnoidal standing wave formula and the Goda's formula overestimate the wave pressure at the wave peak moment. Moreover, the traditional methods of wave pressure for emerged and submerged breakwater give great differences with reality. (2) Wave current fields are similar in the case of quarter-circular type breakwater and semi-circle type breakwater under submerged and emerged conditions. The vortex will last longer with greater strength behind the quarter-circular type breakwater under submerged status. Based on the analysis of the wave pressure results of the two type breakwaters, a wave pressure formula is presented for the quarter-circular type breakwater, which is to calculate wave pressure by the formula for the semi-circle breakwater and then to multiple a modifying factor. Two formula are presented to estimate the reflection and transmission coefficients for the two types of breakwater, respectively.A three dimensional wave numerical model is presented based on spatially- filtered incompressible viscous fluid equations, the level set equations and the concepts of two-phase flow. The partial cell method is adopted to treat the boundary of obstacles. Two-step projection method is used in the solver. The advection term is discretized by combining the upwind and the center difference and the other derivates by center difference. In the calculation, an improved Heaviside function is presented to enhance the accuracy of wave pressure and to avoid oscillation. Waves are generated at the boundary, which can simulate all kinds of theoretical wave such as small amplitude wave, Stokes wave, cnoidal wave and solitary wave. The model is verified in the aspects of water profile, conservation of mass and energy, wave height distribution through the calculational cases of an oscillatory water in two and three dimension box, wave interaction with submerged breakwater and a wave interactionwith large-diameter vertical cylinder. It is found that the model performs very well in conserving mass and energy. The wave profile and current field are consistent with theoretical results. The model can simulate the phenomena of wave action with obstacles. Wave shoaling, secondary wave, reflection, diffraction are all normally reflected by the model. Meanwhile,, some modification and further research to be carried out in the future are indicated.