  A fluid in a non-equilibrium state exhibits long-ranged correlations of its
hydrodynamic fluctuations. In this article, we examine the effect of a
transpiration interface on these correlations -- specifically, we consider a
dilute gas in a domain bisected by the interface. The system is held in a
non-equilibrium steady state by using isothermal walls to impose a temperature
gradient. The gas is simulated using both direct simulation Monte Carlo (DSMC)
and fluctuating hydrodynamics (FHD). For the FHD simulations two models are
developed for the interface based on master equation and Langevin approaches.
For appropriate simulation parameters, good agreement is observed between DSMC
and FHD results with the latter showing a significant advantage in
computational speed. For each approach we quantify the effects of transpiration
on long-ranged correlations in the hydrodynamic variables.
