Academic literature on the topic 'Numerical Relativistic Hydrodynamics'

Hydrodynamics has been successful in providing a good description of the bulk dynamics in ultra-relativistic heavy ion collisions. In this brief review, we provide basics of the theory of viscous hydrodynamics. Topics covered include derivation of the 2nd order viscous hydrodynamics from the linear response theory and kinetic theory, viscous anisotropic hydrodynamics, and numerical implementation of relativistic hydrodynamics.

ABSTRACT We consider the relativistic hydrodynamics of non-perfect fluids with the goal of determining a formulation that is suited for numerical integration in special-relativistic and general-relativistic scenarios. To this end, we review the various formulations of relativistic second-order dissipative hydrodynamics proposed so far and present in detail a particular formulation that is fully general, causal, and can be cast into a 3+1 flux-conservative form, as the one employed in modern numerical-relativity codes. As an example, we employ a variant of this formulation restricted to a relaxation-type equation for the bulk viscosity in the general-relativistic magnetohydrodynamics code bhac. After adopting the formulation for a series of standard and non-standard tests in 1+1-dimensional special-relativistic hydrodynamics, we consider a novel general-relativistic scenario, namely, the stationary, spherically symmetric, viscous accretion on to a black hole. The newly developed solution – which can exhibit even considerable deviations from the inviscid counterpart – can be used as a testbed for numerical codes simulating non-perfect fluids on curved backgrounds.