Research On Theories And Applications Of Non-grid Numerical Simulation In Water Wave Dynamics

N-S equations are the basic equations describing fluid flowing. It is one of the most effective approaches in solving problems of water dynamics to solve them by numerical method under proper boundary conditions. Most of the previous research work used grid methods in solving N-S equations. In this paper, a non-grid method is adopted. Based on several computing examples, the applications of non-grid numerical model are investigated. This subject is not only significant in theory, but also has good prospect of engineering application.At first, the numerical methods related to solve the N-S equations and the turbulent closure schemes are reviewed. Brieve introduction is made on some specifically important methods.One of the main work in this paper is the research of the theories on how to establish the water dynamic numerical flume by using the MPS (moving particle semi-implicit) method. Under non-grid condition, the interaction model among neighboring particles is simulated by kernel function. Based on that, the governing equations are discretized by establishing the smoothing model, the gradient model and the diffusion model. The incompressibility of fluid is implementd by introducing a so-called particle number density.Another important work is to establish a numerical flume by coding programs based on the theory model. One of the key work is to solve the pressure Possion equation. The speed of the programs is greatly increased by using the MICCG (Preconditioned Incomplete Cholesky Conjugate Gradient) method to solve the obtained large sparse symmetric positive-definite matrix. Based on the calculationanal examples, the processes of water flow are investigated. From the successful simulation of the collapsing process of a water column, the impinging force on the rigid structure is obtained. Further more, the generating method of solitary wave in the non-grid numerical flume is studied and the numerical results are compared with analytical ones. The result is proved to be valid.At last, the numerical results are visualized by using Matlab for clearer display.