University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > On numerical conservation of the Poincaré-Cartan integral invariant in relativistic fluid dynamics

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

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  • UserCharalampos Markakis (University of Cambridge; Queen Mary University of London; University of Illinois at Urbana-Champaign)
  • ClockFriday 04 October 2019, 13:30-14:30
  • HouseSeminar Room 1, Newton Institute.

If you have a question about this talk, please contact info@newton.ac.uk.

GCSW02 - Structure preservation and general relativity

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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