Weighted averaged equations for open channel flow modeling

The numerical modeling of open channel flow is highly important in hydraulic engineering practice. Of the existing numerical models, the classical depth-averaged equations are widely used and can meet most engineering requirements of water depth and mean velocity simulation. However, they fail to take into account the vertical details of velocity and pressure, because the equations are based on the assumption of uniform velocity and hydrostatic pressure.;To avoid the difficult task of expanding the governing partial differential equations (PDEs), an indirect scheme is proposed to solve the hydraulic variables through their weighted averaged values. The governing PDEs are generated using a variety of weight functions, and the weighted averages of relevant hydraulic variables are taken as the unknown dependent variables to be solved. Based on the weighted averaged values and their polynomial expansions, a system of linear algebraic equations is generated and the unknown hydraulic variables, or their coefficients, are easily found.;In hydraulic modeling, turbulence models play a very important role. There are numerous turbulence models, from zero-equation algebraic models to two-equation k-epsilon models. Of these, the depth-averaged k-epsilon turbulence model is widely used to complement the depth-averaged Reynolds equations. To complement the proposed weighted averaged Reynolds equations, a new k-epsilon turbulence model is introduced based on the weighted averaging operation over the standard k-epsilon transport equations. The weighted averaged k-epsilon transport equations can be solved using the new indirect scheme proposed previously. The weighted averaged k-epsilon model shows satisfactory performance in complex flow geometries.;The proposed new model provides a valuable option for studying the vertical structure of flow in open channels where only essential vertical detail and accuracy are required, and where data availability, model complexity, or computational efficiency limit the application of fully 3D models.;A new model is proposed in this thesis to address the essential vertical distributions of velocity and pressure, while avoiding the complexity and high computational cost of fully three-dimensional (3D) models. This new model comprises a system of weighted averaged equations developed from corresponding Reynolds equations by performing weighted averaging operations instead of conventional depth-averaging operations. A system of weighted averaged equations, rather than vertical grids, allows for more identifiable hydraulic coefficients for addressing the vertical details. The model can be applied in hydrostatic or nonhydrostatic mode, according to the simulation requirements and flow conditions. It demonstrates satisfactory vertical detail simulations of velocity and pressure, as well as water surface profiles.