基于广义垂线坐标系的三维非结构数学模型及其在珠江口的应用

A generalized vertical coordinate three-dimensional unstructured mesh model with application to Pearl River Estuaries

基于广义垂线坐标变换,构建了非结构网格的三维水动力数学模型。模型采用半隐式有限体积法对控制方程进行数值离散,其中半隐式法用于水位梯度和垂向紊动扩散以及垂向对流项的离散,显式控制体积分法用于水平对流项等的离散。广义垂线坐标系使得模型能够灵活地对垂向网格进行布置,平面非结构网格使得模型能够适应河口海岸复杂的岸线,并可对局部进行网格加密。模型通过具有解析解的风生流和异重流对模型进行检验,应用模型模拟了珠江口的三维潮流过程,计算结果与实测水文数据的比较表明,模型能够较好地模拟珠江河口的盐水楔和三维分层水动力过程。

Based on the generalized vertical coordinate,an unstructured grid numerical method is developed to simulate three-dimensional shallow water flow.The semi-implicated finite difference and finite volume discretization are applied to the momentum equations and conservation equation,such that the model is robust,stable and mass conservation is satisfied both locally and globally.Since unstructured mesh and generalized vertical grid,the proposed numerical model is well suited to fit complicated estuaries and coastal boundaries and yet is sufficiently flexible to set the vertical layers.The test cases of wind-driven currents and lock exchange flow are used to demonstrate the model′s capabilities.Comparisons between numerical results and analytical data are presented.The Pearl River Estuaries is modeled and is verified and calibrated with field measurement data.The computed results mimic the field data well.