The numerical modelling of tide and flood movement in two-dimensional space using implicit finite difference methods
The non-linear hyperbolic partial-differential equations governing long wave propagation in one and two plan dimensions are derived. By application of the Preissmann or 'box' finite difference scheme two numerical models of long wave behaviour are developed. The first, based on the one plan dimensional form of the partial differential equations, is intended for the solution of flood routing problems in natural river systems. The model has two constituent parts. A main channel algorithm reproducing flood wave behaviour in the main channel of the drainage system and a washland algorithm modelling the behaviour of lateral storage ponds on the river banks. The main channel algorithm possesses the ability to handle: natural channel cross-sections, variable distance increments, tributary inflows, calibration with both distance and stage, rating curve boundary conditions, the formation and drowning of controls and the analysis of controls. On completion of development trials the model was used to assess the effect a new road embankment would have on flood levels in the River Aire in Yorkshire. The second, based on the two plan dimensional partial differential equations, employs an alternating direction application of the Preissmann finite difference scheme to model tide and storm surge behaviour in estuaries and coastal seas. Special consideration was given to boundary conditions in the model and these include a moving shore line boundary condition permitting the flooding and drying of sand flat areas to be modelled and a "weir" flow boundary condition, enabling the overtopping of obstructions with a width considerably less than the grid size of the model to be represented. A practical assessment of the model's capabilities was accomplished by simulating tide and storm surge propagation in the Firth of Clyde and Humber Estuary.