Numerical Simulation Of Flow, Sediment And Solute Transport For Discontinuous Problems In Shallow Water

Because of the extensive engineering application background, the numerical study on discontinuous shallow water flows has caused the great interest of many scholars, the discontinuous shallow water flows include the hydraulic jump, tidal bore, the dam break wave, wave transformation etc. The flow processes in natural water body do not exit separately, they are often coupled with the processes of sediment and the pollutant transport, including the contamination transport and transformation with physical and chemical and biological transformation. Among them, the dam break flow and the strong sediment movement induced by dam break flow can cause a significant loss of life and property for the downstream people. Therefore, research on two-dimensional movable-bed mathematical model for dam-break flow and sediment transport has practical significance on the assessment of the disaster caused by dam break and the dam break risk control. On the other hand, with the increasing of environmental pollution, water environment problems have been paid more and more attention. In order to realize the treatment of polluted water body, it is very necessary to understand the water dynamic characteristics and to control the transport mechanism of the pollutant.Firstly, based on the finite volume method and unstructured triangular mesh, a depth-averaged 2D mathematical model for shallow water has been developed in this study. The model is mainly used to simulate the dam break flood with strong discontinuity and bay tidal with complex terrain. A Roe solver and approximate Riemann solutions with second-order accuracy are used to calculate the grid face fluxes in this model. The hydrostatic pressure is put into the source term of momentum equation. A highly-efficient dry-wet processing technology is used to solves the moving-boundary problem of the dry-wet interface. Six typical dam break tests and three bay tidal currents cases are simulated in this study, and the comparison results of experiment and simulation are pretty good. The results demonstrate that this model has strong adaptability and high accuracy of calculation, and illustrate that the model can be used in engineering practice.Based on the above hydrodynamic model, a depth-averaged 2D mathematical model for dam-break flows on erodible beds has been developed by coupling the shallow water equations, sediment transport equation, and bed evolution equation. This model adopts the momentum and continuity equations for turbid water considering vegetation effects, sediment transport and morphological changes. The model is verified against five cases of the laboratory measurements documented in the literature, and the calculation results agree well with the measurement data. The verification shows that the model is able to simulate the evolvement of dam-break flows and the deformation of bed morphology on a complex computational domain with good accuracy. Simulations of the vegetation cases show that the vegetation on a shoal can reduce the velocity of dam-break flows and the erosion on the downstream bed, but it also reduces the local flood discharge capacity, which leads to a certain rise in the upstream water level.Based on hydrodynamic model, coupling the shallow water equations and the advection-diffusion equation for solute transport, we develop a depth-averaged explicit model for flow and solute transport in coastal waters. The improved upwind scheme with high resolution is evaluated to solve the advection term for solute transport. A method with second order accuracy is used for diffusion terms. Firstly, a pure advection problem in a rotating flow field under ideal conditions and a pure diffusion problem in static water are simulated in order to verify the calculation accuracy of the water quality module of this model. Then, this model is applied to simulate the salinity distribution in the Gironde estuary to verify the computational capability of this model under the real terrain conditions. The model is also used to simulate the motion of a solute cloud in the Zhuanghe coastal water. Numerical results show that the model used in this study is successful in the study of hydraulic properties as well as the solute transport process in coastal waters.