Numerical Simulation of Two-dimensional Dam Break--The Method of Characteristics Based on Operator Splitting
|Keywords||dam break space operator splitting characteristics shock-capturing|
The flood resulting from a dam breaking,and opening by break very spillway,and in order to guarantee safe enlarging the outflow of reservoir,spreads quickly and often causes catastrophes. All water impoundment represents a potential risk to life and property. During last century there were more than 200failures of dams greater than 15m high. They have caused huge economic property and life loss. Many people suffered from the catastrophes of dam break.The dam break floods are extremely complex,and are influenced by many kinds of factors. In earlier period,people researched dam break with experiments. With the development of the calculation technique and the advance of the computer,even more workers simulated the problem of dam break with number calculation.Because the equation of shallow water and the equation of inviscid compressible flow have completely similar mathematical forms,a lot of mathematical concepts and methods -including the numerical simulation method of aerodynamics can be used in the research of the shallow wave.The method of characteristics is a method,using a system of compatible partial differential equations in place of the original hyperbolic system of quasilinear partial differential equations to solve. It has a higher precision and clear physics images,can even be applied to test and measure the applicability and precision of some difference methods.In this paper the basic principle of the method of characteristics is described,and is constructed an explicit scheme for dam break simulation of one-dimensional dam instant all break waves flow of a low dam with rectangle section and a huge dam with trapezia section,and of two-dimensional dam instant part break waves flow with simplest space operator splitting. Compared to the theoretic results,the way has higher accuracy and stronger shock-capturing capability,which showed that this method is valid.