DESCRIPTION :
Two adaptive models have been developed to couple Darcy's and Forchheimer's laws more efficiently by selecting the appropriate law locally based on flow velocity. These methods include the sharp-interface model and the regularized model:
* Sharp-interface model: This approach tracks the interface between Darcy and Forchheimer subdomains using a fixed-point algorithm. It iteratively evaluates velocity fields, flags cells as Darcy or Forchheimer, and adjusts the mesh accordingly. Currently, it has only been implemented in one spatial dimension.
* Regularized model: This model introduces a smooth transition zone between Darcy and Forchheimer regions using a regularizing parameter. As this approaches zero, the model is expected to converge to the sharp-interface model, although this convergence remains unproven. Numerical evaluations show that, for the test case Layer 35 of the SPE10 project, only 5%-10% of the cells require Forchheimer's correction to achieve an error below 10% relative to the GFM.
The goal of the research is to leverage these adaptive models for subdomain prediction and combine them with region-based simulations to achieve computational efficiency without significant accuracy loss. The adaptive models can serve as preprocessing tools to identify the subdomains, enabling region-based simulations to apply the appropriate law within each region. By combining subdomain prediction with domain-decomposition methods, the study seeks to determine whether this hybrid approach is accurate and can outperform the global Forchheimer simulation in terms of speed.
The methodology outlined for the thesis includes several key steps:
* Extending and comparing models: The sharp-interface model will be expanded to higher dimensions and systematically compared against the regularized model.
* Predicting subdomains: Two approaches will be explored for predicting Forchheimer and Darcy regions: a mesh-based approach using classification algorithms, and a shape-based approach relying on simplifying assumptions about the geometry of Forchheimer subdomains.
* Combining predictions with simulations: The predicted subdomains will be integrated with region-based simulations using domain decomposition, and the combined model will be validated against benchmark cases.
* Modeling karst systems: For karst aquifers, where flows are highly turbulent and interact with rough conduit surfaces, Forchheimer's law is insufficient. The study will extend the adaptive models to incorporate the Darcy-Weisbach law and adapt the region-based approach to handle karst networks, transitioning from meshes to graph-based representations to account for the heterogeneous and multiscale structure.
Ultimately, the thesis aims to determine whether adaptive modeling approaches, combined with region-based simulations, provide a computationally efficient and accurate alternative to the global Forchheimer model, particularly in complex systems such as karst aquifers.
Keywords: porous media, Darcy's law, Forchheimer's law, adaptive constitutive law, multiphysics coupling
Code d'emploi : Mathématicien (h/f)
Domaine professionnel actuel : Mathématiciens et Statisticiens
Niveau de formation : Bac+5
Temps partiel / Temps plein : Plein temps
Type de contrat : Contrat à durée déterminée (CDD)
Compétences : Intelligence Artificielle, C ++ (Langage de Programmation), Simulation Informatique, Python (Langage de Programmation), Informatique Scientifique, Essais de Fiabilité, Anglais, Algorithmes, Mathématiques Appliquées, Etudes de Terrain, Elaboration des Prévisions, Géométrie, Mathématiques, Analyse Numérique, Simulations
Courriel :
francesco.patacchini@ifpen.fr
quang-huy.tran@ifpen.fr
tran@ifpen.fr
Téléphone :
+3356538679300
Type d'annonceur : Employeur direct
