Description du projet
Résolution des lois de conservation hyperboliques en astrophysique computationnelle
Les systèmes non linéaires d’équations aux dérivées partielles hyperboliques sont caractérisés par des invariants, dont la conservation, y compris au niveau discret, joue un rôle fondamental dans la réduction de la complexité de leurs simulations numériques. De plus, la conservation de la masse et du moment angulaire, la conservation des équilibres stationnaires et mobiles, et l’identification des limites asymptotiques représentent des défis importants. Ces questions sont particulièrement pertinentes dans les applications astrophysiques, telles que les écoulements turbulents autour des trous noirs, les oscillations des étoiles à neutrons, ainsi que la génération et la propagation des ondes gravitationnelles. Financé par le programme d’actions Marie Skłodowska-Curie, le projet SuPerMan développera des méthodes intelligentes de préservation de la structure, indépendantes du système de coordonnées et avec un ordre de précision élevé, pour étudier efficacement l’évolution de l’espace-temps selon la théorie de la relativité générale.
Objectif
SuPerMan proposes the development and efficient implementation of new structure preserving schemes for conservation laws formulated in an elegant and universal form through covariant derivatives on spacetime manifolds.
Indeed, nonlinear systems of hyperbolic PDEs are characterized by invariants, whose preservation at the discrete level is not trivial, but plays a fundamental role in improving the long term predictivity and reducing the computational effort of modern algorithms. Besides mass and linear momentum conservation, typical of any Finite Volume scheme, the preservation of stationary and moving equilibria, asymptotic limits and interfaces still represents an open challenge, especially in astrophysical applications, such as turbulent flows in gas clouds rotating around black holes.
In this project, our focus will thus be on General Relativistic Hydrodynamics (GRHD) for which such Well Balanced (WB) Structure Preserving (SP) schemes have never been studied before. In particular, we plan to devise smart methods, independent of the coordinate system. This will be achieved by directly including the metric, implicitly contained in the covariant derivative, as a conserved variable inside the GRHD model.
This approach will first be tested on the Euler equations of gasdynamics with Newtonian gravity, extending already existing WB-SP techniques to general coordinate systems. All novel features will be carefully proven theoretically. Next, the new schemes will be incorporated inside a massively parallel high order accurate Arbitrary-Lagrangian-Eulerian Finite Volume (FV) and Discontinuous Galerkin (DG) code, to be released as open source. The feasibility of the project is guaranteed by the strong network surrounding the ER, including experts on WB-SP techniques and mesh adaptation (INRIA France), FV-DG schemes and GRHD (UniTN Italy) and computational astrophysics (MPG Germany). This MSCA project will allow the applicant transition to become an independent researcher.
Champ scientifique
Mots‑clés
Programme(s)
Régime de financement
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)Coordinateur
78153 Le Chesnay Cedex
France