Post-Doctoral Research Visit F/M Mesh adaptation for nonlinear dispersive wave propagation

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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.

Starting from the tsunamis free surface water displacement and flow velocity fields which will be known, we will consider using the Boussinesq model UHAINA for simulating propagation and inundation phases. UHAINA [1], is an operational hydrodynamic model, combining high-order solutions (mandatory for a correct representation of dispersion), unstructured meshes and a HPC-devoted programming environment able to deal with the requirement of a real area. UHAINA also offers rapid development capabilities to integrate new approaches (mesh adaptation and embedded approach, see hereafter) to improve tsunami simulation. 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]. In contrast with [6], where the mesh vertices were moved but the connectivity remained fixed, we will investigate metric-based mesh adaptation, where the domain is entirely remeshed in order to optimize both the elements size and orientation. This allows us to change the global number of vertices throughout the simulation when the waves are expanding in the domain. Vertices can be moved between two remeshings to fine tune their location if needed. This sub-task will involve the coupling of the MMG remeshing software with UHAINA. Mesh adaptation full capabilities can only be leveraged when trying to generate the best possible mesh for a given computation: mesh adaptation is then seen as a process to minimize a certain well-chosen error. Driven by this minimization, one expects the simulations to be noticeably more accurate, and even to emphasize flow details usually neglected by standard refinement procedures. The error model is thus key in the adaptation process. We will first evaluate the performance of classic interpolation error based on indicators developed in the continuous mesh framework [2]. However, 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] Barral, N., Olivier, G., Alauzet, F., 2017. Time-accurate anisotropic mesh adaptation for three-dimensional time-dependent problems with body-fitted moving geometries. J. Comput. Phys., 331, 157-187.

[3]- 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, https://arxiv.org/pdf/2307.05816

[5] 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(3):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

• Coupling of MMG with the code UHAINA.

• Evaluation of the performance classic interpolation error.

• Propose new error estimators for non-linear dispersive wave propagation.

• Run large scale simulations of tsunamis in a realistic setting.

Technical skills and level required :

Languages :

Relational skills :

Other valued appreciated :

• Subsidized meals
• Partial reimbursement of public transport costs
• 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.)
• Possibility of teleworking and flexible organization of working hours
• Professional equipment available (videoconferencing, loan of computer equipment, etc.)
• Social, cultural and sports events and activities
• Access to vocational training
• Social security coverage

The gross monthly salary will be 2788€ (before social security contributions and monthly witholding tax).