Fabien Marche - Software

**Uhaina** is an open source HPC numerical platform project dedicated to the approximations of the solutions of fully nonlinear and weakly dispersive free surface shallow water flows. This ongoing project is developped in collaboration with the CNRS/INSMI, Inria teams CARDAMOM and CAGIRE, IMB Bordeaux and EPOC Bordeaux. Main features:

UHAINA: A parallel high performance unstructured near-shore wave model.

XVie Journées Nationales Génie Côtier-Géne Civil , 2018.

Discontinuous Galerkin discretization of Green-Naghdi equations on unstructured simplicial meshes.

Applied Mathematical Modelling , volume 45, pages 840-864, 2017.

A new class of fully nonlinear and weakly dispersive Green-Naghdi models for efficient 2D simulations.

J. Comput. Phys., volume 282, pages 238–268, 2015.

**WaveBox** is a multi-models numerical platform written in C++ dedicated to the approximations of the solutions of several shallow water asymptotics in the surface dimension d=2 with efficient combined Hybridized Discontinuous Galerkin (HDG) and DG methods on general unstructured meshes (**Saint-Venant**, **Boussinesq** and **Green-Naghdi equations** equations). Main features:

Weighted Interior Penalty discretization of fully nonlinear and weakly dispersive free surface shallow water flows .

J. Comput. Phys. , volume 355, pages 285-309, 2018.

Discontinuous Galerkin discretization of Green-Naghdi equations on unstructured simplicial meshes.

Applied Mathematical Modelling , volume 45, pages 840-864, 2017.

A new class of fully nonlinear and weakly dispersive Green-Naghdi models for efficient 2D simulations.

J. Comput. Phys., volume 282, pages 238–268, 2015.

**GNvorti_1D** is a prototype code for the numerical approximations of the **Green-Naghdi** 1DH equations with vorticity solutions, relying on a **Finite-Volume** approach. Il allows to account for the vertical variations of the flow in the presence of vorticity and currents, without any use of 3d equations. It is the basis of current developments in 2DH. Its main features are:

Nonlinear wave-current interactions in shallow water.

Studies in Applied Math., volume 136(4), pages 382–423, 2016.

Special distinction: Highlights of the year 2016 (four papers out of all those published by this journal in 2016 were selected as “Highlights of the Year” for their novelty, quality and importance)

**GN2D** is a numerical resolution code for the 2D **Green-Naghdi** (or fully non-linear Boussinesq)) equations, relying on a hybrid **Finite-Volumes/Finite-Differences** discretization. The main features are

Main publications associated with **GN2D: **

A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model.

J. Comput. Phys., volume 230(4), pages 1479 - 1498, 2011.

Numerical simulation of strongly nonlinear and dispersive waves using a Green-Naghdi model.

J. Sci. Comput., volume 48(3), pages 105-116, 2011.

A new approach to handle wave breaking in fully non-linear Boussinesq models.

Coastal Engineering, volume 67, pages 54--66, 2012.

A new class of fully nonlinear and weakly dispersive Green-Naghdi models for efficient 2D simulations.

**SURF-WB** is a numerical code for the approximations of the **Saint-Venant** 2DH equations' weak solutions, relying on a **Finite-Volume** approach. Its main features are:

This code has been extensively used by several institutes (BRGM -Unité Risques Côtiers et Changements Climatiques-, Hydraulic and Environmental Engineering Department, Pontificia Universidad Catolica de Chile, LEGI Grenoble, EPOC Bordeaux) and for several projects (ANR MISSEVA, ANR MathOcean, ECOS-CONYCIT, JOHANNA, SUBMERSION, ...). The picture above is issued from a simulation of the submersion in Les Bouchôleurs (17, France) (where I grew up ...) during storm Xynthia, 2010 (joined work with Le Roy S., Pedreros R., André C., Paris F., Lecacheux S. and Vinchon C.)

Here are examples of computations performed with SURF-WB:

Animation Gâvres 1 (Visualisation Submersion Urbaine-3D, Ministère de l’Ecologie)

Animation Gâvres 2 (JOHANNA project - BRGM and Fondation MAIF)

Animation Yves et Chatelaillon (SUBMERSION project - BRGM)

Main publications associated with

Evaluation of well-balanced bore-capturing schemes for 2D wetting and drying processes.

International Journal for Numerical Methods in Fluids, volume 53(5), pages 867-894, 2007.

A positive preserving high order VFRoe scheme for shallow water equations: a class of relaxation schemes.

SIAM J. Sci. Comput., volume 30(5), pages 2587-2612, 2008.

Numerical resolution of well-balanced shallow water equations with complex source terms.

Adv. Water Res., volume 32(6), pages 873-884, 2009.

An efficient scheme on wet/dry transitions for shallow water equations with friction.

Computers & Fluids, volume 48(1), pages 192 - 201, 2011.

On the well-balanced numerical discretization of shallow water equations on unstructured meshes.

J. Comput. Phys., volume 235, pages 565--586, 2013.

Coastal flooding of urban areas by overtopping: dynamic modelling application to the Johanna storm (2008) in Gâvres (France).

Natural Hazards and Earth System Sciences, volume 15, pages 2497-2510, 2015.