Finite Volume Method And Its Application Of Tidal Flow Simulation

The widely used 2d equations of tidal flow simulation belong to the shallow water type. When turbulent and dispersive effects are neglected, the shallow water equations become a quasi-linear system of first order hyperbolic partial differential equations. As the development of the computer science, a lot of methods have been used to solve the shallow water equations numerically. The most significant four methods of them are: Finite Difference Method (FDM), Method of Characteristics (MOC), Finite Element Method (FEM) and Finite Volume Method (FVM). In particular, FVM has been extensively studied in recent years, mainly because it appears in some important fields as aeronautical and aerospace engineering. The shallow water equations have the same structure as the compressible Euler Equations, so many theories and techniques of FVM developed in air dynamics have been used to solve the shallow water equations. FVM deals with the conservation form of the equations. It has many advantages over FDS and FEM. FVM combines the simplicity of FDM with the geometric flexibility of FEM. FVM can be applied using an unstructured grid system as FEM. FVM can also capture discontinuities or shocks properly.hi the first part of this paper, Id and 2d shallow water equations' property and characteristic theory are shown. Then, on the basis of this, the principal and the techniques of using of FVM are discussed. A modern second order method of Monotonic Upstream Schemes for Conservation Laws (MUSCL) approach has also been shown. The key problem of using FVM is to estimate the normal flux through each side of a cell. There are several algorithms to estimate this flux, such as Osher method, Flux Vector Splitting (FVS) method and Flux Difference Splitting (FDS).In this paper, two benchmarks of dam break flow simulation have been designed which use rectangle mesh. The purpose of these benchmarks is to test the correctness and the validity of shock capturing of the model. In the last part, a Dayawan bay tidal flow simulation model, which use triangular mesh and second order scheme has been planed. The results showed that the model is valid to simulate the tidal flow simulation and has significant advantages.