A depth-averaged numerical model for simulating heat and fluid flows in vegetated channels

In this thesis, a complex depth-averaged model is developed for simulating heat and fluid flows in vegetated channels, with a capability to simulate dam-break and flooding phenomena. The model is able to simulate both laminar and turbulent flows, it can take the secondary flow effects of any kind into account, it uses the latest developments in porous media science in order to simulate the flow in vegetated zones, and it is able to perform either a dimensional or a dimensionless solution. This depth-averaged model is able to start a solution from scratch or perform a hot start, it uses many innovative techniques to automatically minimize the computational cost for problems which include huge number of computational cells, it uses many innovative techniques for increasing the accuracy of solutions, it supports variety of boundary conditions, it can perform a high-order solution, and it supports several techniques for controlling the residual errors.;As the first step, a two-dimensional numerical code is developed for simulating heat and fluid flows. The transport equations are solved using a collocated unstructured finite-volume scheme. Both numerical and experimental data are extensively used in order to validate the code for various flow conditions. A Multi-Block Local Triangulation (MBLT) technique is developed and successfully applied to several simulations for reducing the absolute magnitude of the oscillations in pressure field. In this technique, a solution for reducing the absolute magnitude of pressure oscillation is innovatively looked for through grid rather than the transport equations for mass and momentum. The MBLT technique can be simply applied to complicated geometries. This property makes the MBLT technique desirable to be used in engineering software.;The validated two-dimensional code is then extended to a depth-averaged code where, the depth-averaged code itself is validated against additional experimental and numerical data. A vorticity equation is also added to the depth-averaged code in order to take the secondary flow effect into account. The depth-averaged transport equations are written in an innovative way, and the source terms due to the channel bed are also discretized with an innovative method. When the water depth is very small, application of these techniques eliminates the oscillations from the profile of water surface. An appropriate choice of grid for the depth-averaged simulations is then suggested through investigating the solution of depth-averaged transport equations on various grids and flow conditions. An innovative method, Total Value – Linearly Interpolated (TV-LI), is also developed for interpolating variables from cells center into the cells faces. This technique reduces the computational cost and, the amount of reduction in computational cost increases when the number of cells increases.;The depth-averaged code is further extended to include the capability to simulate streams with moving boundaries where the position of water edge is a function of time and space. An innovative method is suggested for controlling the water depth in shallow regions in order to prevent formation of zones with spurious negative water depth. An innovative high-order technique is developed for treating the wetting-drying fronts, and is added to the depth-averaged code. This high-order technique eliminates formation of spurious thin layers of water which normally form and extend downstream when a low-order wetting-drying technique is used. As an important advantage of this feature, the solver will solve the transport equations only in actual wet regions. This will keep the computational cost minimized.;The models which are developed in this thesis are aimed to be used for engineering applications such as dam-break and flooding, channel flow, vegetation, and thermal pollution. All models are developed based on sub-program, module, subroutine, and function concepts and, in turn, it is easily possible to extend them to new applications. The two-dimensional model is also extendable to a three-dimensional model. (Abstract shortened by UMI.).