A Higher-Efficient Non-Hydrostatic Finite Volume Model for Strong Three-Dimensional Free Surface Flows and Sediment Transport

In order to accurately simulate strong three-dimensional （3-D） free surface flows and sediment transport, the fully 3- D non-hydrostatic pressure models are developed based on the incompressible Navier-Stokes equations and convection-diffusion equation of sediment concentration with the mixing triangle and quadrilateral grids. The governing equations are discretized with the unstructured finite volume method in order to provide conservation properties of mass and momentum, and flexibility with practical application. It is shown that it is first-order accurate on nonuniform plane two-dimensional （2-D） grids and second-order accurate on uniform plane grids. A third-order approximation of the vertical velocity at the top-layer is applied. In such a way, free surface zero stress boundary condition is satisfied maturely, and very few vertical layers are needed to give an accurate solution even for complex discontinuous flow and short wave simulation. The model is applied to four examples to simulate strong 3-D free surface flows and sediment transport where non-hydrostatic pressures have a considerable effect on the velocity field. The newly developed model is verified against analytical solutions with an excellent agreement.

A New Efficient Finite Volume Modeling of Small Amplitude Free Surface Flows with Unstructured Grid

A staggered finite-volume technique for non-hydrostatic, small amplitude free surface flow governed by the incompressible Navier-Stokes equations is presented there is a proper balance between accuracy and computing time. The advection and horizontal diffusion terms in the momentum equation are discretized by an integral interpolation method on the orthogonal unstructured staggered mesh and, while it has the attractive property of being conservative. The pressure-correction algorithm is employed for the non-hydrostatic pressure in order to achieve second-order temporal accuracy. A conservative scalar transport algorithm is also applied to discretize k - c equations in this model. The eddy viscosity is calculated from the k-c turbulent model. The resulting model is mass and momentum conservative. The model is verified by two examples to simulate unsteady small amplitude free surface flows where non-hydrostatic pressures have a considerable effect on the velocity field, and then applied to simulate the tidal flow in the Bohai Sea.

A Lifting Line Theory for a Three-dimensional Hydrofoil

Prandtl’s lifting line theory was generalized to the lifting problem of a three-dimensional hydrofoil in the presence of a free surface. Similar to the classical lifting theory, the singularity distribution method was utilized to solve two-dimensional lifting problems for the hydrofoil beneath the free surface at the air-water interface, and a lifting line theory was developed to correct three-dimensional effects of the hydrofoil with a large aspect ratio. Differing from the classical lifting theory, the main focus was on finding the three-dimensional Green function of the free surface induced by the steady motion of a system of horseshoe vortices under the free surface. Finally, numerical examples were given to show the relationship between the lift coefficient and submergence Froude numbers for 2-D and 3-D hydrofoils. If the submergence Froude number is small free surface effect will be significant registered as the increase of lift coefficient. The validity of these approaches was examined in comparison with the results calculated by other methods.

SIMULATION OF SEDIMENT DEPOSITION IN A CAVITY WITH FREE SURFACE

Studies of the flow and sediment movement in a cavity with free surface were mostly limited to physical modeling experiments. In this study, the sediment movement is characterized in detail using a 3-D turbulent numerical model. To close the Reynolds equations, the standard k-ε model is employed. The VOF method is adopted to capture the time varying free surface and the porosity method is introduced to deal with the irregular boundary and the varying bed deformation. The computation results agree well with the experimental data in major aspects such as the vertical distribution of the sediment concentration and the deposition topography in the cavity. The comparisons show that this model can well predict the flow structure and the sediment movement and also the river bed deformation in a cavity.

Grid三维曲面构造与显示的算法及实现

由于存在很大的随机性,采用较为简单的加权方法来建立规则网格Grid格式数据体对三维空间地形进行近似描述,利用OpenGL技术构造Grid数据体三维地形,并对构造出的三维空间曲面进行平移、缩放、旋转等自由变换,提供最多6个切面对三维空间曲面进行任意切割的算法,结合地质演化需要,利用双缓存技术实现了地质要素三维曲面动态演化过程。

3-D VARIABLE PARAMETER NUMERICAL MODEL FOR EVALUATION OF THE PLANNED EXPLOITABLE GROUNDWATER RESOURCE IN RE-GIONAL UNCONSOLIDATED SEDIMENTS

In order to correctly evaluate the exploitable groundwater resottrce in regional complex, thick Quaternary unconsolidated sediments, the whole Quaternary unconsolidated sediments are considered as a unified hydrogeological unit and a 3-D unsteady groundwater flow numerical model is adopted. Meanwhile, with the consideration of the dynamic changes of the porosity, the hydraulic conductivity and the specific storage with the groundwater level dropping during the exploitation process, an improved composite element seepage matrix adjustment method is applied to solve the unsteady flow problem of free surface. In order to eva- luate the exploitable groundwater resource in Cangzhou, Hebei Province, the hydrogeological conceptual model of Cangzhou is generalized to establish, a 3-D variable parameter numerical model of Cangzhou. Based on the prediction of the present groundwater exploitation, and by adjusting the groundwater exploitation layout, the exploitable groundwater resource is predicted. The model enjoys features like good convergence, good stability and high precision.

Numerical simulation of 3-D water collapse with an obstacle by FEM-level set method

An interface capturing approach based on a level set function for simulating transient two-phase viscous incompressible flows is applied in this paper. A narrow-band signed distance function is adopted to indicate the phase fields and the interface. The multiphase flow is numerically solved by three stages with finite element method （FEM）： （1） solving a two-fluid Navier-Stokes （N-S） equations over the whole domain, （2） transporting the level set function with the obtained velocity field, （3） the level set function correction through a renormalization with continuous penalization which preserves the thickness of the interface. In this paper, the 3-D water colunm collapse with an obstacle is simulated, which yielded good agreement with the experimental data.

自由曲面上等斜率曲线的跟踪算法

为了提高自由曲面加工质量 ,提出一种等斜率曲线跟踪算法。算法首先利用曲面内部法矢量的连续性 ,采用二分法求出初始点 ,采用密切圆法进行跟踪 ,然后再用梯度法精化。数值计算结果表明 ,该算法具有较高的计算效率和精度 ,能准确地对曲面进行分区处理 。