Fast and high-precision simulation of hydrodynamic and water quality process in river networks

Abstract

To realize a fast and high-precision simulation of unsteady flows and water quality process in river networks, a 1-D mathematical modelling system for free-surface flows and water quality process is developed. In the hydrodynamic model, a θ semi-implicit method is used to discretize the free-surface gradient term in the momentum equation while the Eulerian-Lagrangian method is employed to solve the advection term. To achieve good mass conservation, the finite-volume method is used to discretize continuity equation. Moreover, the resulting hydrodynamic model is unconditionally stable with respect to the gravity wave speed and flow advection. In solving the scalar transport equation, the forward difference is used for discretization in time while the centre-difference is in space. A sub-cycling is introduced to divide the computational time step and improve the stability of water quality model. Therefore, large time steps are allowed in both the hydrodynamic and the transport models. The coupling of the branches of the river networks is solved using a predictioncorrection method. Then, a Gaussian pulse test and a rectangular wave test are employed to demonstrate the accuracy and the efficiency of the system, which will also provide powerful supports for ecological operations of cascade reservoirs in drainage basins.