Generation of conformal polyhedral meshes for CO2 and geothermal simulations

With the emergence of new numerical schemes based on general meshes, new possibilities arise for meshing complex geological environments and thus tackling new challenges for the energy transition, namely CO2 storage and deep geothermal energy. Indeed, polyhedral meshes offer advantages that strongly typed meshes, such as simplicial or hexa-dominant meshes, do not: the quality of the meshes produced does not depend directly on the quality of the faces imposed on the boundaries of the domain or on the internal surfaces, which are essential for representing changes in the environment. Moreover, these meshes can be edited by a wide range of geometric and topological operators.
This PhD builds on the work of Alexandre Marin at IFPEN, who has demonstrated that it is possible to generate Voronoi meshes that take into account a continuous anisotropy field, and thus control and vary the form factors and density of the cells. The PhD student will compare existing approaches in the literature for obtaining conformity to the internal surfaces of the volume of interest with regard to the geological context. He will develop a new method for obtaining conformity with constraints surfaces by adapting the Voronoi mesh optimization or by evolving the energy function used by the latter. These algorithms will be applied to IFPEN geological models and to the 11th SPE CSP model, to produce conformal polyhedral meshes that consider domain anisotropy and areas of interest for simulation.

Keywords: Polyhedral meshes, Voronoï, Optimization, Geometric modeling, CO2 storage, Geothermal energy, Partial differential equations, Numerical simulations

Academic supervisor    Dr Alexandra BAC, Laboratoire d’Informatique et Systèmes 
Doctoral School    ED184 EDMIM, Université d’Aix-Marseille 
IFPEN supervisor    Dr Laurent ASTART, ORCID : 0009-0005-8875-1320
PhD location    IFPEN, Rueil-Malmaison, France, and/or
LIS / Polytech Marseille, Marseille, France
Duration and start date    3 years, starting in the fourth quarter 2025 (Novembre 3)
Employer    IFPEN
Academic requirements    University Master degree in mathematics or computer sciences
Language requirements    English level B2 (CEFR), Willingness to learn French
Other requirements    Optimization, Differential calculus, Computer programming (ideally C++), Computer graphics, Geometric modeling

To apply, please send your cover letter and CV to the IFPEN supervisor indicated here below.