Relativistic viscous hydrodynamics in the density frame: Numerical tests and comparisons

We conduct a numerical study of relativistic viscous fluid dynamics in the density frame for one-dimensional fluid flows. The density frame is a formulation of relativistic viscous hydrodynamics that is first order in time, requires no auxiliary fields, and has no nonhydrodynamic modes. We compare our results to QCD kinetic theory simulations and find excellent agreement within the regime of applicability of hydrodynamics. Additionally, the density frame results remain well behaved and robust near the boundary of applicability. We also compare our findings to the second-order-in-time hydrodynamic theory developed by Bemfica, Disconzi, Noronha, and Kovtun (BDNK) and a well-known M"uller-Israel-Stewart-type hydrodynamics code, music, which is commonly used to simulate heavy-ion collisions.