SHYFEM – Shallow water HYdrodynamic Finite Element Model

SHYFEM – Shallow water HYdrodynamic Finite Element Model is a package that solves the 3D hydrodynamic equations using finite element method on unstructured meshes, that are particularly suitable for applications in areas with a complex geometry and bathymetry such as jagged coasts, islands, fjords, lagoons, estuaries and lakes. Such meshes provide a seamless representation of the physical area in which the processes are object of study, allowing higher resolution only where needed, with consequent ease of computational resources.

  • The numerical formulation is based on linear staggered finite elements, with separate form functions for water level (node based) and transports (element based), that resemble the fashion of B-grid in finite differences case, ensuring mass conservation.  Default time stepping of SHYFEM is semi-implicit, allowing to run the model with courant number > 1.  Vertical discretization is possible with z coordinates, sigma or hybrid sigma on top of z.
  • Numerical simulations with SHYFEM can be initialized with scalar fields (surface elevation, active tracers) and velocities and forced at the surface by wind, mean sea level pressure, air and dew point temperature, cloud cover, ice cover. The model includes an astronomical tidal model that considers semi-diurnal, diurnal and long period constituents.
  • In case of hot start of the simulation, both scalar and vector fields components from the parent model need to be interpolated on the node locations of the grid used by SHYFEM and stored in text files with a specific format.
  • In case of simulation that considers communication with other water bodies, SHYFEM open boundary condition includes water level and nudging of both 3D velocities and active tracers from coarser resolution simulations.  The input files that include open boundary forcings are text files containing scalar fields and component of vector fields interpolated on the nodes that belong to the boundary lines.


  • Federico I, Pinardi N, Coppini G, Oddo P, Lecci R, Mossa M. 2017. Coastal ocean forecasting with an unstructured grid model in the southern Adriatic and northern Ionian seas. Nat Hazards Earth Syst Sci. 17(1):45-59
  • Umgiesser, G., Canu, D.M., Cucco A. 2004. A finite element model for the Venice Lagoon. Development, set up, calibration and validation, Journal of Marine Systems 51(1-4):123-145, DOI: 10.1016/j.jmarsys.2004.05.009


Ivan Federico.

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