Ten years ago, relativistic viscous fluid dynamics was formulated from first principles in an effective field theory framework, based entirely on the knowledge of symmetries and long-lived degrees of freedom. In the same year, numerical simulations for the matter created in relativistic heavy-ion collision experiments became first available, providing constraints on the shear viscosity in QCD. The field has come a long way since then. We present the current status of the theory of non-equilibrium fluid dynamics in 2017, including the divergence of the fluid dynamic gradient expansion, resurgence, non-equilibrium attractor solutions, the inclusion of thermal fluctuations as well as their relation to microscopic theories. Furthermore, we review the theory basis for numerical fluid dynamics simulations of relativistic nuclear collisions, and comparison of modern simulations to experimental data for nucleus-nucleus, nucleus-proton and proton-proton collisions.
PrefaceStrictly speaking, the subtitle of this work is somewhat misleading. Considerable progress on relativistic viscous fluid dynamics had been made earlier than 2007 both in the context of theoretical formulations as well as in numerical simulations. However, in particular for simulations of high energy nuclear collisions, typically an unrealistically high degree of symmetry had been assumed, making the resulting dynamics 0+1d or 1+1 dimensional. Only ten years ago, simulations in 2+1d became available, which is the minimum required to simulate the so-called elliptic flow observed in experiments. As one of the groups that first achieved 2+1d relativistic viscous fluid dynamics simulations ten years ago, we took the opportunity to celebrate this anniversary by compiling the present review of the current status of the field. Given the ongoing vibrant research activity on relativistic viscous fluid dynamics as well as continued experimental developments, we fully expect this review to be outdated in a few years. This is of course good news, and we hope it will require a new review subtitled "Twenty Years of Progress" when the time has come.Happy anniversary, relativistic viscous fluid dynamics!