Description du projet
La concentration de l’attention et des efforts porte ses fruits dans la description des flux géophysiques
Les mathématiques sont le langage que nous utilisons pour décrire le monde physique, et les équations différentielles nous indiquent comment un paramètre change en fonction des modifications d’autres paramètres. Cela peut être utile pour tout, des fluctuations de la pression sanguine au mouvement des toxines dans l’air. Les équations différentielles s’avèrent également très importantes pour la description des problèmes géophysiques, dont beaucoup nécessitent des approximations particulièrement précises de certaines caractéristiques spécifiques de la solution. En se concentrant sur ces dernières à l’aide de méthodes dites stabilisées, il est possible de réduire les augmentations inutiles de la charge de calcul dans des parties moins pertinentes. Avec le soutien du programme Actions Marie Skłodowska-Curie, le projet GEODPG concevra de telles techniques qui contribueront à la séquestration du CO2 dans la terre.
Objectif
The main objective of this project is to design stabilized space-time adaptive techniques based on Discontinuous Petrov-Galerkin (DPG) methodology for the simulation of transient Partial Differential Equations (PDEs), with special emphasis on advection-dominated- diffusion and wave propagation problems. The final goal is to apply the resulting methods to improve the seismic imaging of the Earth’s subsurface for CO2-sequestration, a long-term storage process that contributes to fight climate change and mitigate global warming. In many geophysical problems governed by PDEs, it is important to accurately approximate some specific features of the solution. Goal-oriented adaptive techniques in finite element methods are powerful tools to achieve such goals with optimal computational cost. However, due to the unstable nature of the governing equations in geophysical flows, employing stable discretization methods is crucial in these kinds of algorithms. Stabilized methods such as DPG avoid refinements in unnecessary places of the domain. In this project, we will develop methods, algorithms and a software for transient PDEs employing stable time-marching schemes based on DPG method supporting goal-oriented adaptivity. Finally, we will present the obtained results to several European oil and gas companies in order to apply our method in real world scenarios. The host has an extensive experience in geophysical applications and the Third Country (TC) host is one of the inventors of the DPG method. This set up, together with the applicant’s experience in goal-oriented adaptive algorithms for PDEs, gives the applicant the perfect environment to efficiently develop the proposed project. Moreover, the knowledge and experience acquired during the fellowship will make her a potential applicant to obtain a strong research position in Europe. The host and the TC host will also benefit from the resulting advances on the topic and the industrial collaborations derived from this project.
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MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)Coordinateur
48009 Bilbao
Espagne