SuPerMan
In short
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
Open Positions
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).
Events
International Conference MultiMat 2022:
Tenth International Conference on Numerical Methods for Multimaterial Fluid Flow
22-26 August 2022, Zürich, Switzerland
Journées Calcul & Simulations en Nouvelle Aquitaine
Réunir la communauté Calcul et Simulation de Nouvelle-Aquitaine pour échanger, discuter, collaborer...
6-7 December 2021, Arcachon, France