Research On Spatially-adaptive Numerical Wave Model

Wave hydrodynamics has always been an important object of research in coastal and offshore engineering. The numerical wave flume, which is based on the N-S equations for the incompressible flow, has become an effective tool in hydrodynamics research, which can not only give the process of water surface elevation, but also can provide the information on the complete hydrodynamic field of the whole domain. The research on numerical methods of the governing equations for the incompressible flow with free surface can promote the development of CFD in theory on the one hand, and it can provide an effective method for the prediction of hydrodynamic information in practical projects as well. The main achievements of the research are summarized as follow.(1) The state-of-the-art of CFD are reviewed, including the solution schemes for the N-S equations, the methods of free surface tracking and the methods of dealing with the boundary in the solution of N-S equations. A complete new CFD model is proposed after comparison of the merits and demerits among various CFD models.(2) A new CFD model is proposed, in which the projection method is applied to solving the N-S equations of incompressible fluid, the unconditionally stable MacCormack scheme with second-order accuracy both in time and space is adopted to discretize the advection term and the BI_CGSTAB method is adopted to solve the Poisson equation. The model is not only has high solution efficiency, but also has good accuracy and stability.(3) In the CFD model, FPLS (fast particle level set) method is adopted for the free surface tracking. Being different from others, this method not only has the ability to capture complex topology change of the surface, but also has high accuracy, good property of mass-conservation and fast computation speed. In order to reduce the amount of calculation, the air phase is excluded in the simulation domain, and the governing equations are solved only inside the water zone. Ghost pressure method and equivalence extrapolation method are used to deal with the boundary conditions at the free surface.(4) An adaptive tree mesh structure system is developed, in which the meshes can be split and merge adaptively based on the velocity gradient and the distance from the free surface and the solid boundary. This mesh adaptive technique can save computer memory and computational time effectively, while maintaining high accuracy in the region of interest.(5) 2D and 3D spatially-adaptive numerical wave flumes have been developed, in which internal wave-maker and boundary wave-maker are applied to 2D and 3D models, respectively. Comparison of the modeled results of water surface elevation with the analytical solutions given by the small amplitude wave, cnoidal wave and Stokes wave shows good agreement. Numerical simulations are also carried out for the propagation of waves over a submerged reef and around a square column respectively, and the calculated pressure on the square column is consistent with the result given by the formula of the Code of Hydrology for Sea Port (JTJ-213-98).