Unstructured mesh implementation

Since, the characteristic spatial scales of the wind waves propagating from deep to shallow waters are very diverse, a flexible grid would be required to allow local refinement of the mesh in areas of interest e.g., regions of strong bathymetry variations in estuaries and fjords, without incurring overhead associated with grid adaptation at some distance offshore. Traditionally, this can be achieved by employing a nesting technique. Although, this practise is very common for SWAN, it is generally recognized that this may lead to complicated programming with the corresponding significant increase in computational effort.


The use of unstructured grids, however, offers a good alternative to nested models not only because of the ease of local grid refinement, either adaptive or fixed, but also the high flexibility to generate grids along coastline and around islands. The variable mesh is especially useful in coastal regions where the water depth varies greatly. Thus, the variable grid gives the highest resolution where it is most needed. Moreover, this can be automated to a large extent. Although, the CPU cost per grid point is often relative higher than cases with structured grids, this effect is probably more than offset by the reduction in the number of grid points.


This chapter presents an unstructured grid procedure for SWAN. Details can also be found in (Zijlema, 2009, 2010). The numerical propagation scheme for structured grids is based on a four-direction Gauss-Seidel iteration technique and is accompanied by a fully implicit temporal discretization; see Section 3.3. Hence, SWAN is stable for any time step. Because of this nice property, this solution technique is tailored to unstructured grids.