| Popis: |
Environmental hydraulics covers a very wide range of applications including free surface flows in rivers. estuaries and lakes. To find engineering solutions to environmental hydraulics problems. 3D numerical modelling is nowadays widely used. However. the computation of sharp spatial gradients (such as found in stratified estuaries and lakes. around plumes near outfalls along rivers and coasts or in exchange areas of high shear). and the modelling of these processes along steep bathymetric slopes (such as found at the edge of dredged channels or of the continental shelf) remains a challenge. In addition. crude assumptions (such as the hydrostatic assumption) are often made to the primary differential equations in order to simplify the problem and enable long term prediction of environmental hydraulic changes. \ud \ud In this thesis. a robust adaptive mesh displacement (AMD) method is implemented and validated against the lock exchange case in particular. The AMD method aims at vertically focusing nodes within each water column to capture sharp gradients. while reducing the number of nodes or requiring prior knowledge of the flow structure. Second. a direct computation of dynamic pressure is introduced based on the equation of vertical momentum and validated against the analytical potential flow theory solution of a source-sink pair. Dynamic pressure is necessary to model destratification recirculation devices. or flow over dredge channel. or solitary waves. for instance. This direct computation method makes the hydrostatic assumption redundant. Third. a new advection scheme is implemented. whose main advantage is simplicity averaging over Riemann problems without solving them. while excessive numerical viscosity is compensated for by using high-resolution MUSCL type reconstruction. \ud \ud Recommendations are made in this thesis to extend the advection scheme developed herein for tracer advection to the non-linear shallow water equations. to the diffusion terms and to turbulence closure laws within the same finite element framework. |
