This paper is concerned with a mathematical model for river closure using two embankments. Some novel techniques of computational fluid dynamics and the two equation (k-ε)turbulent model are used to solve the shallow water equations in curvilinear coordinates; and the technique of moving boundary is used to deal with the river bed exposed to water surface. Comparison between computed and experimental data shows a satisfactory agreement. The mathematical model can be employed to accurately simulate the characteristics for the studied flows and could find more applications in hydraulic engineering. Some novel techniques of computational fluid dynamics and the two equation (k-ε) turbulent model are used to solve the shallow water equations in curvilinear coordinates; and the technique of moving comparison between computed and experimental data shows a satisfactory agreement. The mathematical model can be employed to accurately simulate the characteristics for the studying flows and could find more applications in hydraulic engineering.