Development and testing of a subgrid-scale model for moving-boundary hydrodynamic problems in shallow water

Over the past 20 years numerical algorithm advances and increased computing power have led to the development of high-resolution hydrodynamic models for a variety of shallow-water flow problems. Despite the success of these approaches a number of fundamental constraints remain, in particular the simulation of flows that involve rapid changes in the position of the fluid boundary, for example river and coastal floods, tidal flows and dam breaks, is still extremely difficult. Given the relative difficulty of developing deformable meshing techniques that adapt to the flow evolution, most hydraulic models utilize a fixed-grid approach and use a correction algorithm for flow over partially wet elements. A range of techniques are available from simple grid-cell exclusion/inclusion methods to reformulation of the controlling hydrodynamic equations based on a knowledge of the subgrid topography. Although the latter approach retains the most realism, a number of problems with its implementation remain unresolved. These include the lack of a transparent sequence of numerical development and the need for a scheme that incorporates both mass and momentum corrections for partially wet elements. Moreover, in testing the scheme there is a clear requirement for a rigorous and objective test for such problems to be defined. In this paper a new subgrid-scale approach to dynamic wetting and drying in shallow water is therefore developed that overcomes these constraints. In particular a test case consisting of a sinusoidal tide on a planar beach is developed where water depths across the domain at each time-step are known independently of the model and compared with simulations conducted using both standard finite-element methods and the new technique. This comparison demonstrates that the new model gives a significant improvement in predicted hydraulics, particularly on the wetting phase. Moreover, it is shown that the new scheme applied to a low-resolution mesh outperforms standard methods solved using much higher resolution grids. The possibility is also raised that standard methods will always fail to capture wetting and drying processes adequately. This is critical as the simulations conducted show that the accurate capture of such hydrodynamic effects near the boundary has a significant impact on predictions over the entire domain. Copyright (C) 2000 John Wiley & Sons, Ltd.