Consider a fluid of given density $\rho [\frac{kg}{cm^{3}}]$ in thermal equilibrium at a given temperature $T [K]$. If at time $t_{0}$ we apply a force $f(\vec{r}, t) = f_{0}\delta(t-t_{0})\delta(\vec{r}-\vec{r_{0}})$ at position $\vec{r_{0}}$, which options does this impulse have to propagate away from $\vec{r_{0}}$ ? i.e how is this excess of energy transported ?
In the limit of low temperature $T\rightarrow 0$ and high density $\rho>> 1$, a sequence of collisions propagating in the direction of the force $f_{0}$ should be expected where the initial momentum perturbation would be moving as a perturbation front with the acoustic velocity. This would be acoustic transport. In the limit of high temperature $T\rightarrow \infty$ and low density $\rho<< 1$ the "directed and ordered" propagation of the momentum would be hindered by random collisions due to thermal fluctuations, such that momentum would be effectively undergoing random walk or diffusive transport. In this case, the initial momentum perturbation would be flattening roughly as $\delta p\sim\eta t^{\frac{1}{2}}$.
Having these two extreme cases in mind, we now consider a simulated fluid (based on molecular dynamics, boltzmann equation or navier-stokes equation) with periodic boundary conditions (PBC). PBC are used to simulate unbounded fluids and therefore a perturbation such as the one mentioned above should ideally propagate away without being affected by the boundary conditions. In the references mentioned in the answer to this question " Acoustic finite-size effects of simulated fluids under periodic boundary conditions " the authors show that acoustic transport can indeed lead to strong acoustic finite size effects due to the transmission of momentum fluctuations through the periodic boundaries. But could we expect similar diffusive finite size effects ? i.e effects arising due to diffusive transport of momentum perturbations through the periodic boundary ?
