ABSTRACT A new 3D hydrodynamic model was developed to simulate water quality transport in surface waterbodies. The governing equations are the continuity equation, free surface equation, momentum equation and transport equation. The 2D numerical scheme of CE-QUAL-W2 was expanded in three dimensions and modified to solve for the free surface elevation. A time splitting technique was employed to solve the momentum and transport equation. The numerical formulation of the 3D scheme used a novel solution, which resulted in a tri-diagonal matrix form for solving the free surface equation rather than a more computationally intensive penta-diagonal matrix solution. In addition, the hydrodynamic and water quality equations were solved at the same time step in order to allow feedback between water quality and hydrodynamics. The verification of the model hydrodynamics and temperature was performed by comparing the model predictions to known analytical solutions and field data from Lake Chaplain, Washington, USA. There was good agreement of the solution of the hydrodynamic equations to analytical solutions and field data.

中文翻译：

---

基于 CE-QUAL-W2 中的 2D 公式的 3D 水动力和水质数值方案的分析和现场验证

摘要 开发了一种新的 3D 流体动力学模型来模拟地表水体中的水质传输。控制方程是连续性方程、自由表面方程、动量方程和输运方程。CE-QUAL-W2 的二维数值方案在三个维度上进行了扩展和修改，以求解自由表面高程。采用时间分裂技术来求解动量和输运方程。3D 方案的数值公式使用了一种新颖的解法，从而产生了用于求解自由表面方程的三对角矩阵形式，而不是计算量更大的五对角矩阵解。此外，水动力和水质方程在同一时间步长求解，以允许水质和水动力之间的反馈。通过将模型预测与来自美国华盛顿州查普兰湖的已知解析解和现场数据进行比较，对模型的流体动力学和温度进行了验证。流体动力学方程的解与解析解和现场数据有很好的一致性。