Numerical Simulation Of Hydrodynamic And Water Quality Based On WENO Schemes

With the development of numerical technology, the method of numerical simulation has been applied to hydraulic engineering,environmental engineering, and etc. In order to improve the calculation precision for the problem of water environment, the numerical model and the solution method have been renovated.In this paper, a two-dimensional flow-pollutant model has been established based on some recent hydrodynamic model of shallow water. The 2D hydrodynamic and water quality simulation equations have been discretized and solved by the Finite volume method and the WENO scheme. The 2D problem is transfered into a series of local 1D problem by using Gauss-Green formula and the rotational invariance property of the flux.Therefore, the solution process is much simplized. The numerical normal flux of variables across the interface between cells is estimated by the FDS scheme. In order to simulate the flows with high resolution, this paper compares several schemes, and chooses the high distinguishing WENO scheme to treat the hydraulic parameters of the numerical flux in flow equations, and the unsteady term is discretized by Runge-Kutta method. To verify the proposed model flows of dam-break and the transfer of contamination have been simulated. The comparisons between numerical results and the analytical show that the model has high simulation precise, and can meet the environmental engineering requirements. Additionally, the research results have provided a good basis for research of hydrodynamic and water quality in river flows, hydraulic engineering, and etc.