Hydrodynamic modelling practices are greatly enhanced by combining one-dimensional (1-D) and two-dimensional (2-D) models into one overall model. The benefits are: greater efficiency; reduced computation time; greater accuracy; impacts from works are registered in all models; and, improved user satisfaction and performance.
To realise these benefits, a dynamically linked 2-D/l-D hydrodynamic modelling program, codenamed TUFLOW, was developed. It is specifically designed for the modelling of long waves in rivers, estuaries and coastal waters.
For the 1-D component, the ESTRY program was used without any significant modification. ESTRY is an established program, based on an explicit finite difference method (FDM) for the 1-D shallow water equations (SWE). For the 2-D component, new computer code was written to emulate the 2-D SWE solution scheme proposed in Stelling (1984). The Stelling scheme is an alternating direction implicit (ADI) FDM based on the well-known Leendertse (1967, 1970) schemes.
The code written for the 2-D scheme was validated and assessed using a range of test models. The results from the testing found that:
1. Mass was conserved 100 % between internal grid elements.
2. The advection terms in the momentum equation were performing correctly.
3. Water level boundaries were extremely stable, but incorrect results can occur where only water level boundaries are specified, as the discharge across the model’s boundaries is not defined.
4. Flow boundaries were highly unstable for steady state simulations, and where stable, caused a loss of mass of up to 3 % for large Courant Numbers (> 50). They showed good stability in dynamic simulations.
Incorporated into TUFLOW are three significant developments, namely:
1. A method for wetting and drying of 2-D intertidal flats, which allows the continued draining of perched waters.
2. The dynamic linking of any number of ESTRY 1-D network models to a TUFLOW 2-D model.
3. The stabilisation of water level boundaries lying obliquely to a 2-D orthogonal grid, therefore, providing maximum flexibility for locating the 2-D/l-D interface.
A comprehensive computer graphics system was also developed for the purpose of this study, but is not presented as part of this thesis. Aspects of the above developments have been briefly described in Syme (1989, 1990), and Syme and Apelt (1990).
The wetting and drying method developed is shown to calculate the tidal prism more accurately, and to eliminate the occurrence of surges when perched waters are reconnected with the rising tide. Application in practice has shown the method to be a significant improvement over convential methods, especially in models with large areas of intertidal flats.
For dynamically linking the 1-D and 2-D schemes, a simple but effective method is proposed, which utilises the excellent stability properties of the 2-D scheme’s water level boundaries.
The 1-D and 2-D boundaries at the interface are treated as normal open boundaries. A flow boundary is specified for the 1-D model and a water level boundary for the 2-D model. At the end of each computation step boundary condition data is transferred from one model to the other. For the 1-D boundary, the flow across the 2-D model boundary is specified, while for the 2-D boundary the water level from the 1-D model is used.
The conditions at the 2-D/l-D interface are that the water level is approximately horizontal, there is negligible variation in the convective acceleration terms and the flow is perpendicular to the 2-D model boundary. These are essentially the same conditions which are applied at the open boundaries of the 1-D and 2-D schemes.
Testing has shown the 2-D/l-D link to conserve mass 100 % and to have no stability problems. Application to more than twenty production models has shown it to be a very useful and powerful facility.
A key aspect in the successful application of the 2-D/l-D link was the development of a method for stabilising water level boundaries which lie obliquely to the orthogonal 2-D grid. This provides maximum flexibility for locating the interface, which in practice is extremely important, because of the irregularity of natural water bodies.
This thesis presents a discussion on the process of selecting the 1-D and 2-D schemes; and the details of: the methodology used for coding the 2-D scheme; the wetting and drying method; the dynamic 2-D/l-D link; and the stabilisation of oblique water level boundaries. Selected results from test cases are also presented.