Descripción del proyecto
Resolución de leyes de conservación hiperbólicas en astrofísica computacional
Los sistemas no lineales de ecuaciones diferenciales parciales hiperbólicas se caracterizan por presentar invariantes, cuya conservación a nivel discreto desempeña un papel fundamental a la hora de reducir la complejidad de cálculo de sus simulaciones numéricas. Además, la conservación de la masa y del momento angular, la conservación de los equilibrios estacionarios y móviles, y la identificación de los límites asintóticos constituyen temas muy complejos. Estos son especialmente relevantes en aplicaciones astrofísicas como, por ejemplo, los flujos turbulentos alrededor de agujeros negros, las oscilaciones de estrellas de neutrones y la generación y propagación de ondas gravitacionales. En el proyecto SuPerMan, financiado por las Acciones Marie Skłodowska-Curie, se desarrollarán métodos ingeniosos de conservación de estructuras independientes del sistema de coordenadas y con un alto nivel de precisión para estudiar de forma eficaz la evolución del espacio-tiempo según la teoría de la relatividad general.
Objetivo
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.
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MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)Coordinador
78153 Le Chesnay Cedex
Francia