Abstract

On the study of mathematical model for engineering hydraulics and sediment transport research, the complex dynamic boundary is the key point for the calculations, which will directly impact the reliability, accuracy and calculation time of the whole calculation results. To choose the treatment method for the complex dynamic boundary is as important as to choose the numerical method. In this paper, the diagonal Cartesian method simulating the complex boundary, together with the treatment to wetting-drying dynamic variation of the boundary, is applied into the two-dimensional shallow-water flows and sediment transport mathematical modeling, and their governing equations are discretized and solved in diagonal Cartesian coordinates. The model is non-coupling and non-saturating sediment transport, and it can calculate steady and unsteady flow. It adopts ADI method as the numerical method, upwind format when discretizing the equations, orthogonal and uniform mesh as calculation mesh, and special processing program when tracing the dynamic boundary. The study cases of the model with the diagonal Cartesian method have calculated the tidal and sediment transport of the sediment deposition of the Dandong Power Plant’s reservoir at Dadongguo nearby the Yalujiang estuary. The calculated results such as flow field and the distribution of sediment concentration are verified by the measure data. Through the applications and verifications in the engineering projects, it shows that in the two-dimensional flow and sediment transport calculation, the diagonal Cartesian method, together with the dynamic boundary treating method, can simulate the actual boundary and its dynamic variation well, with small error and avoiding saw-tooth boundary; with simple treatment of program design, low quantity of additional calculation, and high calculating efficiency. This method provides a new idea for the complex dynamic boundary calculation and good application prospect.

Keywords: Diagonal Cartesian method, Two-dimensional flow and sediment transport modelling, Study case