基于有限体积法的二维浅水流动数值模拟程序开发

Numerical Simulation of 2D Shallow Water Flow ow Finite Volume Method

应用近年来浅水动力学理论的研究成果,参考国内外在软件设计方面几十年积累的经验,开发了基于有限体积法的二维浅水流动数值模拟程序CFD-FVM2D。程序以Roe格式的近似Riemann解为基础,离散浅水方程并将源项按特征方向进行特征分解,建立带源项浅水方程的通量平衡的Godunov求解格式,并对摩擦源项采用隐式、半隐式求解格式,以解决浅水方程的间断、动边界和河床起伏问题。

This paper develops a kind of 2-D shallow water flow simulation program-CFD-FVM2D based on the finite volume method applying the research results of shallow water hydrodynamics theory which developed in recent years and referencing decades of experience in the software design.The program disperses the shallow water equations and decomposes the source terms in characteristic direction based on approximate Riemann solver of Roe′s scheme,presents the flux balance Godunov scheme for the shallow water equation with source terms.The implicit and half-implicit scheme are used to solve friction term of the source terms in order to solve the problems that discontinuity,moving boundary and bed level changes of the shallow water equations.