Study Cases Of Diagonal Cartesian Method For Two-dimensional Mathematical Model Of Flows And Suspended Sediment Transport

On the study of mathematical model for engineering hydraulics and sedimenttransport research, the complex dynamic boundary is the key point for thecalculations, which will directly impact the reliability, accuracy and calculation timeof the whole calculation results. To choose the treatment method for the complexdynamic boundary is as important as to choose the numerical method. In this paper,the diagonal Cartesian method simulating the complex boundary, together with thetreatment to wetting-drying dynamic variation of the boundary, is applied into thetwo-dimensional shallow-water flows and sediment transport mathematical modeling,and their governing equations are discretized and solved in diagonal Cartesiancoordinates.The model is non-coupling and non-saturating sediment transport, and it cancalculate steady and unsteady flow. It adopts ADI method as the numerical method,upwind format when discretizing the equations, orthogonal and uniform mesh ascalculation mesh, and special processing program when tracing the dynamicboundary.The study cases of the model with the diagonal Cartesian method havecalculated the tidal and sediment transport of Quanzhou bay in Fujian province, theflood development of Xiaozhong river in Beijing, the sediment transport andpollutant diffusion of the Yangtze River segment at Zhenjiang in Jiangsu province, theblocking influence on flow due to the bridge across Yongding river in Beijing, thesediment deposition of the reservoir at Dadonggou in Liaoning province, and the flowand sediment transport due to wind of 13-tombs reservoir in Beijing. And the modularprogramming is added into the original program to calculate fetching or drainingwater, sediment or pollutant discharge, and wind influence correspond to therequirement of the engineering. The calculated results such as flow field and thedistribution of sediment concentration are verified by the measure data, and furthercalculation and analysis is on the laws of flow movement, suspended sedimenttransport and pollutant diffusion in research regions under various natural (such asflood and ebb tides of various ranges, floods of various frequencies, winds of variousdirections and velocities, storm surge, etc.) and man-made conditions (includingbeach inning, port and bridge buildings, engineering acquirement for water, sedimentdischarge, oil leakage of ships, and so on), providing scientific foundation for thedecision-making and optimization of corresponding engineering constructions.Through the applications and verifications in the engineering projects above, itshows that in the two-dimensional flow and sediment transport calculation, thediagonal Cartesian method, together with the dynamic boundary treating method, cansimulate the actual boundary and its dynamic variation well, with small error andavoiding saw-tooth boundary;with simple treatment of program design, low quantityof additional calculation, and high calculating efficiency. This method provides a newidea for the complex dynamic boundary calculation and good application prospect.