中文摘要：

目前水动力学问题的数值求解仍然广泛采用RANS模型,特别对于大尺度的地表水流的数值模拟,该类模型计算效率较高,但其难以给出湍流场的小尺度涡结构.深入研究复杂地形条件下的水流运动,需要发展诸如LES等的高级数值模型.天然地表水流,地形、边界复杂,雷诺数通常较高,高级数值模拟受限于计算能力的限制,还难以工程应用.RANS和LES混合模型是目前具有工程应用的一种混合数值模型,其已经在CFD领域获得了长足发展.然而对于地表水流运动的数值模拟,相关工作还较少.本文将分离涡模型（DES）,即一种RANS和LES的混合模型,应用于带自由表面的地表水流运动,建立了一套数值仿真模型.模型基于有限体积法,水平面内采用非结构计算网格,垂向为结构化网格,对流项离散格式采用二阶TVD格式,并行基于OpenMP语言库.算例表明DES模型有助于揭示复杂地形条件下带自由表面水流的大涡拟序结构.

英文摘要：

Geophysical flows in oceanic shelves,estuaries,and rivers are often studied with the shallow water equations under either hydrostatic or hydrodynamic pressure assumptions.The Reynolds-Averaged Navier Stokes （RANS） equations are widely used for simulating the complex turbulent flows because of their high efficiency.The Directed Numerical Simulation （DNS） and Large Eddy Simulation （LES） are commomly unaffordable under the constraint of the present computer power.In practical applications,one kind of hybrid models,i.e.Detatched-Eddy Simulation （DES）,is a good compromise because of the lower computational cost for simulating near-wall flows with RANS.In the paper,a DES model is proposed based on a fully hydrodynamic pressure model instead of hydrostatic model.The numerical scheme is based on the Finite Volume Method （FVM） on unstructured grids in the horizontal plane,and the σ coordinate in the vertical direction to fix the free surface and the uneven bottom.The in-house codes are paralleled using OpenMP.The proposed model is shown to be particularly effective in the prediction of small-scale vortical structures.