Project description
Solving hyperbolic conservation laws in computational astrophysics
Nonlinear systems of hyperbolic partial differential equations are characterised by invariants, whose preservation also on the discrete level plays a fundamental role in reducing the computational complexity of their numerical simulations. Furthermore, the conservation of mass and angular momentum, the conservation of stationary and moving equilibria, and the identification of asymptotic limits are challenging issues. These are especially relevant in astrophysical applications, such as turbulent flows around black holes, oscillations of neutron stars and generation and propagation of gravitational waves. Funded by the Marie Skłodowska-Curie Actions programme, the SuPerMan project will develop smart structure preserving methods independent of the coordinate system and with high order of accuracy, to effectively study the evolution of spacetime in general relativity.
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.
Fields of science
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Programme(s)
Funding Scheme
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)Coordinator
78153 Le Chesnay Cedex
France