- It is based on an explicit, second order finite difference method for staggered grids whereby mass and momentum are strictly conserved at discrete level. As a consequence, this simple and efficient scheme is able to track the actual location of incipient wave breaking. Also, momentum conservation enables the broken waves to propagate with a correct gradual change of form and to resemble steady bores in a final stage. Yet, this approach is appropriate for hydraulic jumps, dam-break problems and flooding situations as well.
- In the case of flow contractions, the horizontal advective terms in momentum equations are approximated such that constant energy head is preserved along a streamline.
- By considering the similarity between breaking waves and moving hydraulic jumps, energy dissipation due to wave breaking is inherently accounted for. In addition, nonlinear wave properties under breaking waves such as asymmetry and skewness are preserved.
- For accuracy reason, the pressure is split-up into hydrostatic and non-hydrostatic parts. Time stepping is done in combination with a projection method, where correction to the velocity field for the change in non-hydrostatic pressure is incorporated. Moreover, space discretization precedes introduction of pressure correction, so that no artificial pressure boundary conditions are required.
- Because of the abovementioned pressure splitting, hydrostatic flow computation can be done easily as well by simply switching off the non-hydrostatic pressure. As such, SWASH is appropriate for the simulation of large-scale tides and storm surges.
- With respect to time integration of the continuity and momentum equations, the second order leapfrog scheme is adopted, as it does not alter the wave amplitude while its numerical dispersion is favourable. This will prove beneficial to wave propagation.
- Alternatively, time discretization may take place by explicit time stepping for horizontal advective and viscosity terms and semi-implicit time stepping using the -method for both surface level and pressure gradients as well as the free-surface condition. As a consequence, unconditional stability is achieved with respect to the celerity of gravity waves. The enhanced stability of this time stepping allows larger time steps, by a factor of five to ten, compared to the leapfrog scheme, and may thus be beneficial to large-scale applications such as tidal flow, and wind and density driven circulation.
- The physical domain can be discretized by subdivision of the continuum into cells of arbitrary shape and size. A structured grid is employed, which means that each interior cell is surrounded by the same number of cells. A distinction is made between the definition of the grid in the horizontal and vertical direction. In the horizontal planes, rectilinear or orthogonal curvilinear, boundary-fitted grid can be considered. Either Cartesian coordinates on a plane or spherical coordinates on the globe can be defined. In the vertical direction, the computational domain is divided into a fixed number of layers in a such a way that both the bottom topography and the free surface can be accurately represented. In this way, it permits more resolution near the free surface as well as near the bed.
- In order to resolve the frequency dispersion up to an acceptable level of accuracy, a compact difference
scheme for the approximation of vertical gradient of the non-hydrostatic pressure is applied in conjunction
with a vertical layer mesh employing equally distributed layers.
This scheme receives good linear dispersion up to
*kd*8 and*kd*16 with two and three equidistant layers, respectively, at 1% error in phase velocity of primary waves (*k*and*d*are the wave number and still water depth, respectively). The model improves its frequency dispersion by simply increasing the number of vertical layers. - The three-dimensional simulation of flows exposing strong vertical variation amounts to the accurate computation of vertical turbulent mixing of momentum and some constituents, such as salt, heat and suspended sediment, combined with an appropriate vertical terrain-following grid employing sufficient number of non-equidistant layers. The vertical variation may be generated by wind forcing, bed stress, Coriolis force or density stratification.
- The combined effects of wave-wave and wave-current interaction in shallow water are automatically included and do not need any additional modelling, such as calculating the radiation stresses explicitly and subsequently solving a wave-averaged hydrodynamic model separately.
- For a proper representation of the interface of water and land, a simple approach is adopted that tracks the moving shoreline by ensuring non-negative water depths and using the upwind water depths in the momentum flux approximations.

Like SWAN, the software package of SWASH includes user-friendly pre- and post-processing and does not need any special libraries (e.g. PETSc, HYPRE). In addition, SWASH is highly flexible, accessible and easily extendible concerning several functionalities of the model. As such, SWASH can be used operationally and the software can be used freely under the GNU GPL license (http://swash.sourceforge.net).