Development of Numerical Methods for dispersive free surface flows in an applicative framework

The Inria center at the University of Bordeaux is one of the nine Inria centers in France and has about twenty research teams.. The Inria centre is a major and recognized player in the field of digital sciences. It is at the heart of a rich R&D and innovation ecosystem: highly innovative SMEs, large industrial groups, competitiveness clusters, research and higher education players, laboratories of excellence, technological research institute...

This project is a part of the ANR project LAGOON and the regional PSGAR project CORALI. The selected candidate will have to implement numerical strategies to deal with dispersive free surface models, in the Uhaina software. The Uhaina software, based on the Aerosol library (C++, parallelized, Discontinuous Galerkin Runge Kutta (DG-RK) scheme), aims at constructing a platform for the simulation of near shore hydrodynamics.

Two improvements of the current scheme will be implemented. First we will focus on an Explicit-Implicit (ImEx) scheme do deal with low-Froude regime [4]. At low-Froude regime, the classical scheme becomes very diffusive and the CFL condition is very restrictive. ImEx schemes are ideal for this purpose. Secondly, we will implement dispersive source terms in the software. Dispersive models are an improvement on the well-known hyperbolic model for shallow waters, to give a better estimate of wave propagation speeds. Several numerical strategies are currently described in the literature: pseudo-compressible [1], elliptic source term [2], prediction-correction [3]. We will focus on a prediction-correction method based on projection of a linear subspace. First-order and second-order schemes will be implemented.

References

[1] N. Favrie and S. Gavrilyuk. A rapid numerical method for solving Serre–Green–Naghdi equations describing long free surface gravity waves. Nonlinearity, 30(7):2718, 2017.

[2] M. Kazolea, A. G. Filippini, and M. Ricchiuto. Low dispersion finite volume/element discretization of the enhanced Green–Naghdi equations for wave propagation, breaking and runup on unstructured meshes. Ocean Modelling, 182:102157, Apr. 2023.

[3] M. Parisot. Entropy-satisfying scheme for a hierarchy of dispersive reduced models of free surface flow. International Journal for Numerical Methods in Fluids, 91(10):509–531, 2019.

[4] M. Parisot and J.-P. Vila. Centered-potential regularization for the advection upstream splitting method. SIAM Journal on Numerical Analysis, 54(5):3083–3104, 2016

• Implementation of updated numerical schemes of ImEx numerical scheme for shallow water model in a real-life context.

• Implementation of updated numerical schemes for Boussinesq-type models in a real-life context

• Design and run characteristic test cases for continuous integration.

• Write scientific reports

• Solid knowledge on C++ language, software version control with Git and software design.

• Solid knowledge in classical numerical scheme (for hyperbolic and/or elliptic equations).

• Basic knowledge in classical PDE.

• Taste for environmental problems, mathematical formalism and numerical simulations.

• Language: English (Speaking, writing and reading).

• Restauration subventionnée
• Transports publics remboursés partiellement
• Congés: 7 semaines de congés annuels + 10 jours de RTT (base temps plein) + possibilité d'autorisations d'absence exceptionnelle (ex : enfants malades, déménagement)
• Possibilité de télétravail partiel et aménagement du temps de travail
• Équipements professionnels à disposition (visioconférence, prêts de matériels informatiques, etc.)
• Prestations sociales, culturelles et sportives (Association de gestion des œuvres sociales d'Inria

Contrat à durée déterminée

Rémunération brute selon diplômes et expériences : de 2692 euros à 3084 euros