Constraining relativistic viscous hydrodynamical evolution

We show that by requiring positivity of the longitudinal pressure it is possible to constrain the initial conditions one can use in second-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 second-order viscous hydrodynamical evolution equations appropriate to describe the evolution of matter in an ultrarelativistic heavy-ion collision.