ausblenden:
Schlagwörter:
Astrophysics, High Energy Astrophysical Phenomena, astro-ph.HE,General Relativity and Quantum Cosmology, gr-qc
Zusammenfassung:
MHD turbulence is likely to play an important role in several astrophysical
scenarios where the magnetic Reynolds is very large. Numerically, these cases
can be studied efficiently by means of Large Eddy Simulations, in which the
computational resources are used to evolve the system only up to a finite grid
size. The resolution is not fine enough to capture all the relevant small-scale
physics at play, which is instead effectively modeled by a set of additional
terms in the evolution equations, dubbed as sub-grid-scale model. Here we
extend such approach, commonly used in
non-relativistic/non-magnetic/incompressible fluid dynamics, applying the
so-called gradient model to a general set of balance-law equations, that
includes the relevant case in which a non-trivial inversion of conserved to
primitive fields is needed. In particular, we focus on the relativistic
compressible ideal MHD scenario, providing for the first time (and for any
equation of state) all the additional sub-grid-scale terms. As an application,
we consider box simulations of the relativistic Kelvin-Helmholtz instability,
which is also the first mechanism responsible for the magnetic field
amplification in binary neutron star mergers and cannot yet be fully captured
by the finest-grid and longest simulations available. The performance of our
model is numerically assessed by comparing it to the residuals arising from the
filtering of high-resolution simulations. We find that the model can fit very
well those residuals from resolutions a few times higher. Although the
application shown here explicitly considers the Minkowski metric, it can be
directly extended to general relativity, thus settling the basis to implement
the gradient sub-grid model in a GRMHD binary merger. Our results suggest that
this approach will be potentially able to unveil much better the small-scale
dynamics achievable in full GRMHD simulations.
