Modeling flow and pressure distribution by multilayer averaged equations

多层模型实际上是多层平均动量方程（类似于深度平均方程）的解。多层系统的优点之一是，由于这种相似性，可以从任何二维深度平均程序建立三维多层模型。为了升级任何深度平均模型，应该在动量方程中加入额外的项，以解释层之间的摩擦和质量传递。动量方程可以用类似的方法求解每一层。在此步骤之后，流深度被更新，迭代过程继续，直到实现收敛。一些研究人员也将多层法应用于明渠，假设水平层的厚度不变。这种假设对河道流动造成了一定的限制，因为顶层必须容纳所有的水面变化，它可能变得太厚，在不同的位置模型精度降低。另一个复杂情况是，当下层水流与河床地形相交时，施加的边界条件变得非常复杂。本文提出的模型结合多层建模和深度平均方程，在层选择和湍流模型上进行了修改，成为多层深度平均模型。该模型不同于经典的多层模型和经典的深度平均模型，不仅可以模拟平均流速和流深，还可以预测深度上的流速和剪切剖面。该模型将被修改和扩展，以模拟弯曲明渠中的水力跳跃和流动。利用其他三维水动力模型将模拟结果与实验数据和数值结果进行比较。这将验证该模型是否具有在复杂的三维流动条件下预测流动的能力。

A multilayer model is in fact the solution of layer averaged momentum equations (which are similar to depth averaged equations) in a number of layers. One of the advantages of a multi-layer system is that due to this similarity, a three-dimensional multilayer model can be developed from any two-dimensional depth-averaged program. To upgrade any depth-averaged model, additional terms should be added to the momentum equations to account for friction and mass transfer between the layers. The momentum equations can be solved in a similar manner for each layer. Following this step, the flow depth is updated and the iteration process continues until convergence is achieved. A few researchers have also applied the multilayer method in open channels with the same assumption of horizontal layers of constant thickness. This assumption causes some restriction in channel flows since the top layer must accommodate all of the water surface variation, it may become too thick and model accuracy is reduced in different locations. An additional complication occurs when the lower layers of flow intersect the bed topography and the imposing boundary conditions become very complicated.  The proposed model proposed herein incorporates the multilayer modeling and depth-averaged equations to become the multilayer depth averaged model with modifications in layer selection and turbulence model. The model differs from classical multilayer models and classical depth averaged models so that the proposed model will simulate not only the averaged velocities and flow depth but also predict the velocity and shear profiles over the depth. The model will be modified and expanded for simulations of hydraulic jump and flow in curved open channels. Modeling results will be compared with experimental data and numerical results by other three-dimensional hydrodynamatic models. These will verify whether the model has the capability to predict flows in complex three-dimensional flow conditions.