BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Michael Dumbser (University of Trento) DTSTART:20250526T134000Z DTEND:20250526T151000Z DTSTAMP:20260405T175331Z UID:NSCM/177 DESCRIPTION:Title: O n well-balanced finite difference\, finite volume and discontinuous Galerk in schemes for the Einstein-Euler system of general relativity\nby Mic hael Dumbser (University of Trento) as part of Nečas Seminar on Continuum Mechanics\n\nLecture held in Room K3\, Faculty of Mathematics and Physic s\, Charles University\, Sokolovská 83 Prague 8..\n\nAbstract\nIn this t alk we present a new family of well-balanced conservative CWENO finite dif ference schemes and discontinuous Galerkin (DG) finite element schemes wit h subcell finite volume (FV) limiter for the numerical solution of the Ein stein–Euler equations of general relativity based on a first order hyper bolic reformulation of the Z4 formalism. The first order Einstein-Euler Z4 system\, which is composed of 64 equations\, is analysed and proven to be strongly hyperbolic for a general metric. The well-balancing is achieved for arbitrary but a priori known equilibria by subtracting a discrete vers ion of the equilibrium solution from the discretized time-dependent PDE sy stem. Special care has also been taken in the design of the numerical visc osity so that the well-balancing property is achieved. As for the treatmen t of low density matter\, e.g. when simulating massive compact objects lik e neutron stars surrounded by vacuum\, we have introduced a new filter in the conversion from the conserved to the primitive variables\, preventing superluminal velocities when the density drops below a certain threshold\, and being potentially also very useful for the numerical investigation of highly rarefied relativistic astrophysical flows.\n\nWe furthermore prese nt a novel family of central WENO finite difference schemes for a new firs t order reformulation of the classical BSSNOK system.\n\nThanks to these i mprovements\, all standard tests of numerical relativity are successfully reproduced\, reaching four main achievements: (i) we are able to obtain st able long term simulations of stationary black holes\, including Kerr blac k holes with extreme spin\, which after an initial perturbation return per fectly back to the equilibrium solution up to machine precision\; (ii) a ( standard) TOV star under perturbation is evolved in pure vacuum (ρ = p = 0) up to t = 1000 with no need to introduce any artificial atmosphere arou nd the star\; and\, (iii) we solve the head on collision of two punctures black holes\, that was previously considered untractable within the FO-Z4 formalism\, (iv) we perform a stable long-time evolution of a rotating bin ary black hole merger based on the new CWENO schemes for first order refor mulation of the BSSNOK system.\n\nReferences\n\n[1] M. Dumbser\, O. Zanott i\, E. Gaburro and I. Peshkov\, A well-balanced discontinuous Galerkin met hod for the first–order Z4 formulation of the Einstein–Euler system\, Journal of Computational Physics 504 (2024)\, 112875.\n\n[2] M. Dumbser\, O. Zanotti and I. Peshkov. High order discontinuous Galerkin schemes with subcell finite volume limiter and AMR for a monolithic first-order BSSNOK formulation of the Einstein-Euler equations\, Physical Review D 110 (2024) \, 084015.\n\n[3] M. Dumbser\, O. Zanotti and G. Puppo\, A monolithic firs t–order BSSNOK formulation of the Einstein–Euler equations and its sol ution with conservative finite difference CWENO schemes\, Physical Review D\, submitted.\n LOCATION:https://researchseminars.org/talk/NSCM/177/ END:VEVENT END:VCALENDAR