复杂地形上坝堤溃决洪水演进的非结构有限体积模型

针对复杂地形上坝堤溃决洪水演进的二维数值模拟,综合考虑底坡项、摩阻项和干湿界面对水流的影响,基于浅水二维水动力学理论建立了非结构有限体积模型.围绕传统底坡项处理技术应用于复杂地形时的不足,通过计算底坡项对物质通量和动量通量的影响,并进行相应的分解,提出了集成底坡项的近似Riemann求解器.分析并采用改进的隐式格式解决了摩阻项可能引起的刚性问题.通过求解干湿单元界面处"镜像湿单元"Riemann问题,结合变量重构技术,有效处理了动边界问题.算例研究结果表明,模型稳定健全,和谐性好,具有较好的推广应用价值.

An Unstructured Finite-volume Model for Dam/Dyke Break Floods with Complex Topography

According to the two-dimensional numerical simulation of dam/dyke break flood propagation over complex topography,an unstructured finite-volume model,which integrates the source terms and the moving wet/dry fronts,was developed based on the two-dimensional shallow hydrodynamics.To overcome the shortage of conventional techniques for treating bed slope term when facing convoluted topography,the influence of bed slope term both on mass flux and on momentum flux was investigated,and then an approximate Riemann solver which integrates the bed slop terms was adopted to calculate the numerical fluxes.The stiff problem due to friction terms was analyzed,and a semi-implicit scheme was used to deal this stiff problem.The moving boundary problem was managed effectively by using a new reconstruction method and solving a "mirror wet cell" Riemann problem at the wet/dry front.Numerical results of test examples showed that the proposed model was stable and robust,and was well balanced,thus having a bright application prospects.