ALcHyMiA
Financiado
Advanced Structure Preserving Lagrangian schemes for novel first order Hyperboli...
Advanced Structure Preserving Lagrangian schemes for novel first order Hyperbolic Models: towards General Relativistic Astrophysics
ALcHyMiA will make substantial progress in applied mathematics, targeting long-time stable and self-consistent simulations in general relativity and high energy density problems, via the development of new and effective structure...
ALcHyMiA will make substantial progress in applied mathematics, targeting long-time stable and self-consistent simulations in general relativity and high energy density problems, via the development of new and effective structure preserving numerical methods with provable mathematical properties. We will devise innovative schemes for hyperbolic partial differential equations (PDE) which at the discrete level exactly preserve all the invariants of the continuous problem, such as equilibria, involutions and asymptotic limits. Next to fluids and magnetohydrodynamics, key for benchmarks and valuable applications on Earth, we target a new class of first order hyperbolic systems that unifies fluid and solid mechanics and gravity theory. This allows to study gravitational waves, binary neutron stars and accretion disks around black holes that require the coupled evolution of matter and spacetime. Here, high resolution and minimal dissipation at shocks and moving interfaces are crucial and will be achieved by groundbreaking direct Arbitrary-Lagrangian-Eulerian (ALE) methods on moving Voronoi meshes with changing topology. These are necessary to maintain optimal grid quality even when following rotating compact objects, complex shear flows or metric torsion. They also ensure rotational invariance, entropy stability and Galilean invariance in the Newtonian limit. The breakthrough of our new Finite Volume and Discontinuous Galerkin ALE schemes lies in the geometrical understanding and high order PDE integration over 4D spacetime manifolds. The high-risk high-gain challenge is the design of smart DG schemes with virtual, bound-preserving, genuinely nonlinear data-dependent function spaces, taking advantage of the Voronoi properties. Finally, it is an explicit mission of ALcHyMiA to grow a solid scientific community, sharing know-how by tailored dissemination activities from top-level schools to carefully organized international events revolving around personalized interactions.
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Duración del proyecto: 59 meses
Fecha Inicio: 2024-04-01
Fecha Fin: 2029-03-31
Fecha Fin: 2029-03-31
Línea de financiación: concedida
El organismo HORIZON EUROPE notifico la concesión del proyecto el día 2024-04-01
Línea de financiación objetivo
El proyecto se financió a través de la siguiente ayuda:
ERC-2023-STG:
ERC STARTING GRANTS
Cerrada
hace 2 años
Presupuesto
El presupuesto total del proyecto asciende a
2M€
Líder del proyecto
UNIVERSITA DEGLI STUDI DI VERONA
No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico
TRL
4-5
Perfil tecnológico
TRL
4-5