SuPerMan

MSCA-IF funded project under the Horizon 2020 programme, grant agreement No 101025563.
Period: 01/06/2021 -- 31/05/2023.

Abstract.
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), FVDG schemes and GRHD (UniTN Italy) and computational astrophysics (MPG Germany). This MSCA project will allow the applicant transition to become an independent researcher.

Main results.
4 accepted papers + 1 paper submitted + 1 book chapter + 1 proocedings

Available 1 PhD position: the online open call is available at this link!
Title: High order Lagrangian Discontinuous Galerkin schemes on moving Voronoi meshes for the solution of hyperbolic equations
Application deadline: 9 of Mai 2023
Feel free to contact me if you need any further information!

Available soon: 3 to 6 months internships will be available soon (contact me if you are interested).
Filled position: 1 year postdoctoral position.

People interested in not yet open positions should send an email to elena.gaburro@inria.fr, including a detailed CV, 2 to 6 months before their preferred starting date.

Possible research topics include: lagrangian schemes on moving meshes with topology changes (for example: parallelization, moving boundaries, adaptive mesh refinement, new applications, 3D extension ...) and well balancing for general relativity (using simplified or complete models, in 1D, 2D or 3D, with a theoretical and/or a numerical approach).