|Numerical simulation of free surface flows with steep gradients|
María Busnelli, M. (2001). Numerical simulation of free surface flows with steep gradients. Communications on Hydraulic and Geotechnical Engineering, 01-3. TU Delft. Faculty of Civil Engineering and Geosciences: Delft. x, 180 pp.
Part of: Communications on Hydraulic and Geotechnical Engineering. Delft University of Technology. Department of Civil Engineering: Delft. ISSN 0169-6548, more
Dam design; Flow; Free surface; Modelling; Numerical methods; Numerical models; Simulation
Dike breaches; Dijkbreuken
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A phenomenon common to hydraulic engineering is that of free surface flows with steep water or bed level gradients. The simulation of these flows is something that is of general practical interest to the management of water resources in both lowland and mountain river basins. For example, as a consequence of a dam break, a bore will be generated that will propagate through the domain. The height and speed of the bore are critical parameters in flood control. Other examples are man-made hydraulic structures such as spillways, stilling basins, check dams and flood control channels, which are characterised by high velocities and hydraulic jumps. High velocities and local hydraulic jumps occur in mountain streams due to the steep slopes and the strong natural geometrical changes.
The problems mentioned above involve abrupt changes in the flow in time and space. In such discontinuous flows it is essential to conserve properties. This imposes strong restrictions upon numerical schemes to simulate those kind of hydraulic engineering problems. Implicit algorithms like those developed for coastal regions and estuaries, although efficient for subcritical flows, are not effective for these types of flows. In the literature, a different class of numerical schemes has been applied to solve discontinuous flows, the so-called Godunov methods, which are in general explicit and based upon nonstaggered grids. A disadvantage of Godunov-type schemes resides in the treatment of the non-homogenous terms of the shallow water equations, because property conservation could be seriously violated. Furthermore, extensions to solve the full Reynolds-averaged Navier-Stokes equations become complicated and involve the inclusion of an artificial compressibility term to obtain hyperbolic equations.
In this thesis a semi-implicit numerical scheme is presented for conservation laws in order to simulate flows with steep water and bed level gradients in multi-dimensions. The numerical scheme combines the ability of the explicit schemes, such as the Godunov-type schemes, to capture steep gradients, and the computational efficiency of the implicit schemes. A numerical method is outlined to solve the fully 3D non-hydrostatic equations. Several applications illustrate the potential of the model, namely: the simulation of the vertical structure of free and submerged hydraulic jumps downstream of a structure, the simulation of the flow due to a dam break, the simulation of the morphological behaviour upstream of open check dams and the simulation of breach growth in dikes. A ID morphological model was developed to predict the morphological behaviour upstream of open check dams. The model was also applied to simulate discontinuous bed profiles in the form of the deformation of a hump and trench.
The presented semi-implicit numerical algorithm is computationally efficient, robust and relatively easy to implement in multi-dimensions. The numerical model constitutes a useful tool for designing hydraulic engineering structures and for flood control systems, both for lowland and mountain areas.