Anisotropic mesh adaptation for nonlinear dispersive water wave propagation in coastal areas

Anisotropic mesh adaptation for nonlinear dispersive water wave propagation in coastal areas

Le descriptif de l’offre ci-dessous est en Anglais

Contrat renouvelable : Oui

Niveau de diplôme exigé : Thèse ou équivalent

Autre diplôme apprécié : PostDoc

Fonction : Ingénieur scientifique contractuel

A propos du centre ou de la direction fonctionnelle

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...

Mission confiée

Natural hazards like earthquakes, volcanoes, landslides, and tsunamis pose unpredictable risks with
significant social and economic impacts. They are unpredictable and the submarine environment
makes direct measurements extremely difficult. In this context, numerical simulations constrained
with high quality geological data provide the unique tool to propose efficient risk reduction strategies.
Disasters, like the Sumatra tsunami in 2004, the Tohoku tsunami in 2011, the Anak Krakatau volcano
tsunami in 2018 or even the very recent Hunga tsunami, are reminders that such phenomena still
need to be studied to reinforce our risk reduction strategies by innovative predictive models.
The goal of this project is the design and implementation of numerical schemes that will deal efficient
with the different spatial scales during the propagation and inundation phases of the tsunamis.
In order to numerically solve the mathematical equations that characterize free surface flows, a
mesh which subdivides the domain into a conformal tesselation is often used. The distribution and
shape of the elements which comprise the mesh can be adapted based on various methods to
distribute computational resources such that areas of higher complexity are given more resolution.
Static meshes, despite being refined a-priori around the coastline, are inherently not efficient for
tsunami simulations where an impulsive wave is initially concentrated in a narrow region and then
propagates over a certain distance. Mesh adaptation techniques have proved their efficiency in
improving numerical accuracy while reducing the overall computational cost in many scientific
domains. Several adaptive strategies have already been deployed for shallow water flows, including
tsunami applications: hierarchical mesh refinement [3,4], unstructured re-meshing [3,5] and r-
adaptation [6].

Resently, we worked on metric-based anisotropic mesh adaptation for the non-linear shallow
water equations in the presence of wet-dry fronts [2], demostrating its suitability for predicting coastal
run-up from incident waves. We used the hydrostatic code UHAINA [1] coupled with the MMG
remeshing software, and developed a tailored error indicator and a simple wet-dry interface
treatment for solution transfer.
We now aim to extend this work to dispersive coastal flows. The dispersive regularization of the
SWE results in more regular solutions, for which classic error models may be limited. A key point of
the project will be to propose error estimators well suited for non-linear dispersive wave propagation.
To our best knowledge, such an error model would be completely novel. In particular, local
smoothness of the solution will first be considered, then we will study phase errors and ways to
control them. We have to highlight that, up to the authors’ knowledge, mesh adaptation for dispersive

wave propagation is, up to now, only limited on structured meshes [4,7] and this will be the first time
unstructured meshes will be used. Once the adaptive process has been validated on academic test
cases, we will run large scale simulations of tsunamis in a realistic setting.

[1] Filippini, A.G., et al., 2018, UHAINA, XVèmes Journés Nationales Génie Côtier - Génie Civil,
DOI:10.5150/jngcgc.2018.006.
[2] Yuan, D., Kazolea, M., Barral, N., Ricchiuto, M., Anisotropic mesh adaptation for the non-linear shallow
water equations, Wallwork, J. G., Barral, N., Kramer, S., Ham, D., Piggott, M., 2020. Goal-oriented error estimation and mesh
adaptation for shallow water modelling. SN Applied Sciences, Springer Verlag, 2-6.
[4]- Berger, M.J., & LeVeque, R. J.,Implicit adaptive mesh refinement for dispersive tsunami propagation,
Blaise, S. & St-Cyr. A., A dynamic hp-adaptive discontinuous Galerkin method for shallow water flows on the
sphere with application to a global tsunami simulation. Mon. Weather Rev., 140:978--996, 2012.
[6] - Arpaia, L., & Ricchiuto, M., 2020. Well balanced residual distribution for the ALE spherical shallow water
equations on moving adaptive meshes. J. Comput. Phys., 405, 109173.
[7] Popinet, S., 2015. A quadtree-adaptive multigrid solver for the Serre–Green–Naghdi equations. J Comput.
Phys., 302,336-358

Principales activités

Main activities

1. Propose new error estimators for non-linear dispersive wave propagation.
2. Validate the new method against classical benchmarks from the literature.
3. Run large scale simulations of tsunamis in a realistic setting.
4. Contribute to open-source code development.
5. Publish scientific articles in peer-reviewed journals and presentations to intentional conferences

Compétences

Technical skills and level required :

The candidate must have a PhD in applied mathematics and scientific computing.

Knowledge in programming (C, C++, Python) will be highly appreciated.

Languages : English at good working level.

Avantages

6. Subsidized meals
7. Partial reimbursement of public transport costs
8. Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
9. Possibility of partial teleworking and flexible organization of working hours
10. Professional equipment available (videoconferencing, loan of computer equipment, etc.)
11. Social, cultural and sports events and activities
12. Access to vocational training
13. Social security coverage

Rémunération

depending on qualifications and professional experience