A Couple Mathematical Models of the Water Quality Measurement in a Stream using Upwind Implicit Methods

Abstract

Two numerical simulations are being used to quality of the water in a non-uniform flow stream. The first model is a hydrodynamic model that uses the Crank-Nicolson formula to provide velocity profile and level of water. The second phase is a dispersion model, where the governing function uses advection-dispersion-reaction equations to provide the concentrations of contaminants. The first and second models are described as one-dimensional equations. The first determined flow velocity profile of the hydrodynamic model shall be the input into the dispersion model at each phase. The finite difference methods are proposed to solve the dispersion model a four points explicit upwind schemes, a third order Crank-Nicolson schemes, and the four points implicit methods, which give the approximated pollutant concentrations. Finally, we present a numerical simulation of all schemes, so as to illustrate their applicability to real-world problems. The proposed topic is related and economic to be used in real-world challenges relatively low cost of the program and the straight-forwardness of its implementations. It is also good to achieve suitable places and easier timeframes for different discharge locations.