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The emergent fluctuating hydrodynamics of a viscoelastic fluid modeled by themultiparticle collision dynamics (MPC) approach is studied. The fluid iscomposed of flexible, Gaussian phantom polymers, which interact by localmomentum-conserving stochastic MPC collisions. For comparison, the analyticalsolution of the linearized Navier-Stokes equation is calculated, whereviscoelasticity is taken into account by a time-dependent shear relaxationmodulus. The fluid properties are characterized by the transverse velocityautocorrelation function in Fourier space as well as in real space. Variouspolymer lengths are considered---from dumbbells to (near-)continuous polymers.Viscoelasticity affects the fluid properties and leads to strong correlations,which overall decay exponentially in Fourier space. In real space, thecenter-of-mass velocity autocorrelation function of individual polymersexhibits a long-time tail independent of polymer length, which decays as$t^{-3/2}$, similar to a Newtonian fluid, in the asymptotic limit $t \to\infty$. Moreover, for long polymers an additional power-law decay appears attime scales shorter than the longest polymer relaxation time with the same timedependence, but negative correlations, and the polymer length dependence$L^{-1/2}$. Good agreement is found between the analytical and simulationresults.

Hydrodynamic correlations of viscoelastic fluids by multiparticle collision dynamics simulations