Constraining relativistic viscous hydrodynamical evolution

TL;DR

This paper introduces a method to constrain initial conditions in relativistic viscous hydrodynamics simulations by enforcing positivity of longitudinal pressure, with explicit demonstration in 0+1 dimensions and extensions to higher dimensions.

Contribution

It provides a novel constraint based on pressure positivity for initial conditions in 2nd-order viscous hydrodynamics, including an analytic approximation for evolution equations.

Findings

Positivity constraint restricts initial conditions in hydrodynamics.

Analytic approximation accurately describes 0+1 dimensional evolution.

Extension of constraints to higher dimensions discussed.

Abstract

We show that by requiring positivity of the longitudinal pressure it is possible to constrain the initial conditions one can use in 2nd-order viscous hydrodynamical simulations of ultrarelativistic heavy-ion collisions. We demonstrate this explicitly for 0+1 dimensional viscous hydrodynamics and discuss how the constraint extends to higher dimensions. Additionally, we present an analytic approximation to the solution of 0+1 dimensional 2nd-order viscous hydrodynamical evolution equations appropriate to describe the evolution of matter in an ultrarelativistic heavy-ion collision.