A new finite volume algorithm to solve the two dimensional shallow water equations on an unstructured
triangular mesh has been implemented in the open source ANUGA software, which is jointly developed
by the Australian National University and Geoscience Australia. The algorithm supports discontinuouselevation,
or `jumps in the bed profile between neighbouring cells. This has a number of benefits compared
with previously implemented continuous-elevation approaches. Firstly it can preserve stationary states at wetdry
fronts without using any mesh porosity type treatment. It can also simulate very shallow frictionally
dominated flow down sloping topography, as typically occurs in direct-rainfall flood models. In the latter situation,
mesh porosity type treatments lead to artificial storage of mass in cells and associated mass conservation
issues, whereas continuous-elevation approaches with good performance on shallow frictionally dominated
flows tend to have difficulties preserving stationary states near wet-dry fronts. The discontinuous-elevation
approach shows good performance in both situations, and mass is conserved to a very high degree, consistent
with floating point error.
A further benefit of the discontinuous-elevation approach, when combined with an unstructured mesh, is that
the model can sharply resolve rapid changes in the topography associated with e.g. narrow prismatic drainage
channels, or buildings, without the computational expense of a very fine mesh. The boundaries between such
features can be embedded in the mesh using break-lines, and the user can optionally specify that different
elevation datasets are used to set the elevation within different parts of the mesh (e.g. often it is convenient to
use a raster DEM in terrestrial areas, and surveyed channel bed points in rivers).
The discontinuous elevation approach also supports a simple and computationally efficient treatment of river
walls. These are arbitrarily narrow walls between cells, higher than the topography on either side, where
the flow is controlled by a weir equation and optionally transitions back to the shallow water solution for
sufficiently submerged flows. This allows modelling of levees or lateral weirs much finer than the mesh size.
A number of benchmark tests are presented illustrating these features of the algorithm. All these features
of the model can be run in serial or parallel, on clusters or shared memory machines, with good efficiency
improvements on 10s-100s of cores depending on the number of mesh triangles and other case-specific details
