ABSTRACT
Regular and irregular mesh solvers for the depth averaged Navier-Stokes equations discretise a 2D domain into cells and faces. Many solution schemes consider the cells and faces to be flat-bottomed and either ‘wet’ or ‘dry’ depending on whether the water surface elevation exceeds the cell or cell face elevation. This approach can be a very simplified representation of the terrain or bathymetry within the cell that potentially causes inaccuracies and a dependency on mesh size, and in the case of regular mesh solvers, mesh orientation, and in the case of irregular mesh solvers, mesh design. A more physically accurate representation is to consider ‘partially wet cells’, that use the underlying topography for each cell and face to build non-linear relationships. In the case of cells, between the cell water volume and the water surface elevation, and in the case of faces, between the water surface elevation and the face flux area. The benefits of ‘sub-grid sampling’ (SGS) appear significant and far-reaching. For whole-of-catchment models, response times and water retention are more realistic. For deep sided channels that are not mesh aligned, flow patterns have no “saw-tooth” effects and obey Manning’s formula. However, most significantly, the sensitivity of results to mesh size is greatly reduced and the sensitivity to mesh orientation is almost eliminated. This conclusion is far-reaching in that regular cartesian mesh solvers can produce the same quality of results as well-designed, high resolution, irregular meshes. The SGS methodology is presented, supported by benchmarking to theory, a flume test and case study observations.
