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Contexte et atouts du poste

This position is part of the Lagoon project (https://vperrier.gitlabpages.inria.fr/lagoon/), which gathers INRIA Bordeaux, BRGM, and UPPA, and which aims at developing a numerical tool for the stormsurges predictions.
This position is opened at UPPA (https://www.univ-pau.fr/en/home.html) within the CAGIRE team (https://team.inria.fr/cagire/), and will be supervised by Vincent Perrier (https://vperrier.perso.univ-pau.fr/).

Mission confiée

When dealing with low Mach number or low Froude number flow, the acoustic waves are propagating much faster than the material waves. When dealing with explicit time stepping, this induces a very small time step. If acoustics plays a minor role in the application, then it is relevant to resort to Implicit-Explicit (ImEx) methods such as [3], in which part of the nonlinear system is integrated implicitly in time, which usually induces the inversion of a system that may be linear or nonlinear depending on the implicit formulation used.

The aim of this position is to address the resolution of such a (non)linear system by developing efficient aggregated geometric multigrid methods. The work addressed will be very diverse:
- Jacobi methods for the implicit wave system,
- study of aggregation strategies for geometric multigrid methods,
- Development of curl preserving spatial numerical scheme [1,2] to aggregated polygonal grids,
- Nonlinear full approximation scheme (FAS) for nonlinear shallow water or isothermal Euler equations.

References
[1] Perrier, V., Development of discontinuous Galerkin methods for hyperbolic systems that preserve a curl or a divergence constraint, available at https://arxiv.org/abs/2405.04347
[2] Perrier, V., Discrete de-Rham complex involving a discontinuous finite element space for velocities: the case of periodic straight triangular and Cartesian meshes, available at https://arxiv.org/abs/2404.19545
[3] Parisot, M. and Vila, J.P. (2016), Centered-Potential Regularization for the Advection Upstream Splitting Method, SIAM Journal on Numerical Analysis.

Principales activités

- Bibliographic studies
- Development of numerical methods
- Numerical implementation
- Writing article and presentation at national and international conferences

Compétences

- a Phd in scientific computing, numerical analysis or fluid mechanics.
- a background in implementation of numerical methods in a compiled language (e.g. C, C++, Fortran).
- a background in numerical methods for hyperbolic systems (Wave system, Euler, shallow-water) is not necessary but would be welcome
- a background in iterative methods for solving linear systems is not necessary but would be welcome

Avantages

• subsidized meals
• partial reimnursement of public transport costs
• possibility of partial teleworking and flexible organization of working hours
• professional equipment avilable (videoconferencing, loan of computer equipment...)
• social, cultural and sports events and activities
• access to vocational training

Rémunération

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