Limiters for spectral propagation velocities in SWAN

As phase-averaged spectral wave models continue to grow in sophistication, they are applied more frequently throughout the ocean, from the generation of waves in deep water to their dissipation in the nearshore. Mesh spacings are varied within the computational domain, either through the use of nested, structured meshes or a single, unstructured mesh. This approach is economical, but it can cause accuracy errors in regions where the input parameters are under-resolved. For instance, in regions with a coarse representation of bathymetry, refraction can focus excessive wave energy at a single mesh vertex, causing the computed solution to become non-physical. Limiters based on the Courant–Friedrichs–Lewy (CFL) criteria are proposed for the spectral propagation (refraction and frequency shifting) velocities in SWAN. These limiters are not required for model stability, but they improve accuracy by reducing local errors that would otherwise spread throughout the computational domain. As demonstrated on test cases in deep and shallow water, these limiters prevent the excessive directional turning and frequency shifting of wave energy and control the largest errors in under-resolved regions.