Lattice Boltzmann Method for relativistic hydrodynamics

By Alessandro Gabbana   Zoom ID: 896 2772 7941     Passcode: 809669

The study of relativistic hydrodynamics has received renewed interest in recent years, as it has been realized that phenomena in diverse areas of physics, such as astrophysics, quark gluon plasma and even condensed matter physics can be studied via a hydrodynamic approach  in the relativistic regime. For example, quark-gluon plasmas (QGP) created in heavy-ion collisions at RHIC or LHC or electron flow in 2D graphene sheets can be considered, in some cases, as relativistic fluids.  For a long time, relativistic fluid dynamics has been hampered by several theoretical and computational shortcomings,  since relativistic versions of Navier-Stokes equations suffer from causality problems linked to the order of the derivatives appearing in the dissipative terms. Some of these problems can be avoided by employing a lattice kinetic approach, that treats space and time on the same footing (i.e., via first-order derivatives).
This is one of the main reasons why Relativistic Lattice Boltzmann Methods (RLBMs), that discretize in coordinate and momentum space the Boltzmann equation, and yet ensure that the resulting synthetic dynamics retains all its hydrodynamic properties, have been recently proposed as effective computational tools to study relativistic flows.
This talk presents an overview of the formal algorithmic derivation of a RLBM capable of handling a wide range of physics parameters and kinematic regimes, from ultra-relativistic to mildly relativistic and eventually to the non-relativistic limit. Moreover, a few examples of applications will be discussed, including cross-comparisons with other numerical methods in the study of relativistic shock waves in QGP.

Large-EDDY-simulations in binary neutron star  mergers

by Carlos Palenzuela.  Meeting ID: 886 0167 6852   Password: 680019

One of the most important open issues in the theoretical understanding of binary neutron star collisions is the amplification of magnetic fields after the merger. This happens first in a turbulent way at small scales via  Kelvin-Helmholtz instability, followed by a large-scale ordering via winding and magneto-rotational instability. However, the highest numerical resolution achieved in full GRMHD simulations O(10m) are extremely expensive (tens of millions of CPU hours) and are still far from capturing all the scales at play, possibly of a meter or less. Here we present how large-eddy-simulations with the gradient sub-grid-scale model can reproduce the magnetic amplification up to local values of 10^17 G during the first 10 milliseconds after the merger, but at a much lower computational cost. This results anticipates a more accurate simulations in the near future with reachable current resources.