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On numerical conservation of the Poincaré-Cartan integral invariant in relativistic fluid dynamics

Presented by: 
Charalampos Markakis
Date: 
Friday 4th October 2019 - 13:30 to 14:30
Venue: 
INI Seminar Room 1
Abstract: 
The motion of strongly gravitating fluid bodies is described by the Euler-Einstein system of partial differential equations. We report progress on formulating well-posed, acoustical and canonical hydrodynamic schemes, suitable for binary inspiral simulations and gravitational-wave source modelling. The schemes use a variational principle by Carter-Lichnerowicz stating that barotropic fluid motions are conformally geodesic, a corollary to Kelvin's theorem stating that initially irrotational flows remain irrotational, and Christodoulou's acoustic metric approach adopted to numerical relativity, in order to evolve the canonical momentum of a fluid element via Hamilton or Hamilton-Jacobi equations. These mathematical theorems leave their imprints on inspiral waveforms from binary neutron stars observed by the LIGO-Virgo detectors. We describe a constraint damping scheme for preserving circulation in numerical general relativity, in accordance with Helmholtz's third theorem.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons