SuPerMan · Structure Preserving schemes for Conservation Laws on Space Time Manifolds
Horizon 2020 — Marie Skłodowska-Curie Actions
- Duration
- 2021-06-01 → 2023-05-31
- EU contribution
- €184,708
- Participants
- 1
- Scheme
- MSCA-IF
Lines connect the coordinator with its partners.
Results in brief
Structure Preserving schemes for Conservation Laws on Space Time Manifolds
In this research project our main objective concerns the development and the efficient implementation of new structure preserving high order numerical methods to solve complex systems of hyperbolic partial differential equations. A special interest is devoted to systems written in covariant form, i.e. independent of the chosen coordinate system, describing phenomena on general spacetime manifolds. This is the case for some reformulations of simple Newtonian systems (such as Euler and Shallow Water equations) used in this project to benchmark our schemes. In addition, this is in particular the case for the systems of equations which describe astrophysical events as i) the General Relativistic Magneto-Hydrodynamics (GRMHD) system which describes the matter dynamics of for example neutron stars and accretion disks, according to a general metric; and this metric can be fixed or we can consider its evolution described by the ii) Einstein field equations of general relativity. Being able to numerically simulate these complex systems could reveal novel information about the origin and the future of our Universe, and also increase our ability in modelling valuable events on Earth. However, these systems are particularly challenging because i) they contain many complex unknowns and ii) their stability could be easily compromised by the accumulation of numerical errors. For these reasons the use of high order of accuracy or fine meshes alone, as done in standard codes, represents an unpracticable solution. Thus SuPerMan wants to incorporate in these codes additional structure preserving capabilities, that, in addition to accurately solving the equations, preserve exactly, at the discrete level, some physical and geometrical invariants of the studied continuum model.
Data: CORDIS, © European Union
Project objective
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.
Original text from CORDIS.
Participants
- INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET AUTOMATIQUE · Le Chesnay CedexCoordinatorFrance
Links
Data: CORDIS, © European Union