TOols Library for unstructured Ocean models and Surge Applications


Tolosa is a research project to develop an efficient open source simulation software for free surface flow, especially for marine flooding previsions, including wave modeling using new Boussinesq-type model and associated numerical resolution.

The main contributions are the software layer the mathematical background to propose efficient simulations considering unstructured grids, much more flexible and efficient to consider complex shorelines and to adapt the size cells to the physics wanted to be capture.

It is implemented original numerical schemes with:

  • global stability by entropy dissipation.
  • low dissipation, especially in high frequencies.
  • respect to the asymptotic low Froude number property.

The software is developed in Fortran 2008 with a KISS principle (Keep It Stupid and Simple) and with some OOP (Object-oriented programming) features.

A library called Tolosa-lib is used at the top to numerically solve each model on unstructured meshes in a CPU MPI parallel environment. It mainly includes:

  • the mangement of partionned unstructured meshes taking care to data locality for enhanced computation speed.
  • some structures to handle as simply as possible the Inputs/Ouputs in parallel including list of parameters, command line interface, VTK, Tecplot, Yaml, CSV, etc …


Tidal in Atlantic Ocean

Saint Malo bay

A wave with a 1 minute period and 1 meter amplitude is enforced at boundaries.

2 solitons in a closed basin

Test case

  • The computational domain is 100 km long.
  • The water depth is 1000 meters at the inflow before large deformations of the bathymetry considering Gaussian as a basis function.
  • The time simulation is 1 hour.
  • A wave with a 2 minutes period and a 1 meter amplitude is enforced at bottom/left boundary, and walls are considered on others.


  1. Richard GL. An extension of the Boussinesq-type models to weakly compressible flows. European Journal of Mechanics - B/Fluids 2021 : 217–240.
  2. Duran A, Vila J-P, Baraille R. Energy-stable staggered schemes for the shallow water equations. Journal of Computational Physics 2020 ; 401 : 109051.
  3. Couderc F, Duran A, Vila J-P. An explicit asymptotic preserving low Froude scheme for the multilayer shallow water model with density stratification. Journal of Computational Physics 2017 ; 343 : 235–270.
  4. Duran A, Vila J-P, Baraille R. Semi-implicit staggered mesh scheme for the multi-layer Shallow Water system. Comptes Rendus Mathématique 2017 ; 355 : 1298–1306.
  5. Parisot M, Vila J-P. Centered-potential regularization for the advection upstream splitting method. SIAM Journal on Numerical Analysis 2016.