基于半隐欧拉-拉格朗日法盐水入侵数学模型

A Saltwater Intrusion Model Based on Semi implicit Eulerian-Lagrangian Finite volume Method

摘要:

建立了适合河口复杂边界的二维潮流盐度数学模型.其中，网格模块是通过多元最小二乘重构的无结构三角网格；潮流模块基于消除了稳定性条件限制的半隐的欧拉-拉格朗日法，并用干湿判断法实现动边界的处理；盐度输运模块采用有限体积法进行离散，并通过用周围单元平均浓度值重构界面浓度的方法得到与连续性离散方程相协调的二阶对流扩散离散方程.通过纯对流和纯扩散数值测试对模型进行了验证，结果表明模型能够较好地模拟盐度输运的对流扩散问题，且具有较高的精度.最后，将模型应用于长江口盐水入侵的模拟计算，计算结果表明：模型计算的潮位、流速和盐度过程与实测资料一致.

Abstract:

A 2D numerical model to simulate tidal flow and salinity in complex estuaries is developed. The grid module is designed under unstructured triangular grid with second order accuracy by cell reconstruction using multiple least square methods to remove stability limitations associated with surface gravity wave. The circulation module is based on semi implicit Eulerian Lagrangian method and free from CFL condition constraint, and the wetting and drying are addressed by movable boundary techniques. The salinity module is designed in the frame work of finite volume method with a second order resolution in coordination with the discreted continuity equation, through the cell face concentration reconstructed from surrounding cell averaged by complex interpolation combined with a mono tonicity criterion. The model has been tested by a pure advection case and a pure diffusion case, which demonstrates that the model has a high accuracy. Finally, this model has been applied to simulating the saline intrusion in the Yangtze (Changjiang)River Estuary and the results show that the simulated tidal levels, velocities and salinities agree well with the measured ones.