| In the field of numerical simulation on broad and shallow waters, two-dimensional mathematical model has its irreplaceable advantages. And it is all the time one of the focuses on calculating hydraulic engineering application. In this paper, the theory and methods on two-dimensional hydrodynamic numerical simulation has been studied more systematically, and several important issues closely associated with numerical simulation have been also explored. Aimed at the characteristic of lateral confluence flow, a corresponding two-dimensional hydrodynamic simulation system has been established. Then, it has been applied to conduct a special numerical simulation on Hong River reaches cross the main canal inverted siphon project of the Middle Line of South-North Water Transfer Project.In this paper the author has carried on the discussion and practical application on the district interpolation methods of complex terrain. Moreover, the author has discussed the flow discontinuity in hydraulic jump region of stilling pool of lateral flow in Wuliu Channel, then a kind of numerical simulation method simplified in hydraulic jump region of open channels was put forward. According to the energy dissipation character of hydraulic jump and water momentum equation (hydraulic jump equation), conjugate relations between upstream and downstream water depth could be basically confirmed. And energy loss in hydraulic jump region could be confirmed by water energy equation.In the model, through the method by roughening (guarantee similar resistance) the front and back reach of stilling pool, continuity of water energy loss and occurrence of water depth after hydraulic jump was realized in the reach of stilling pool. The simulation results show that the simplified method is reliable and practical. It can reflect the relation between conjugate water depth and energy loss, therefore it is able to perfectly solve the problem of flow simulation in Wuliu Channel lateral torrential flow.Many kinds of project plans were numerically simulated on the river reaches with projects and lateral flow in the paper. Backwater and scour situation nearby the inverted siphon project were analyzed here. Then, the location and width of inverted siphon project were also evaluated in the paper. Meanwhile, the author analyzed the impact that Wuliu Channel's lateral flow on the nearby fields of inverted siphon project as following: Firstly, it made the velocity in confluence area bigger, mainstream band wider and move to the right bank. Secondly, it caused the left river bank of Wuliu Channel's downstream to produce recirculation region. In order to improve the confluence condition, the author adjusted cross shape of exit mouth in Wuliu Channel and conducted numerical simulation to find a suitable cross-section shape, which reduced the negative effects on flow field conditions and the riverbed deformation near inverted siphon water drainage project after the intersection of two flows. The established 2-D flow-sediment numerical model has effectively solved the problem of providing design of river projects with technical parameters.
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