Red supergiants (RSGs) are evolved massive stars in a stage preceding core-collapse supernova. Understanding evolved-phases of these cool stars is key to understanding the cosmic matter cycle of our Universe, since they enrich the cosmos with newly formed elements. However, the physical processes that trigger mass loss in their atmospheres are still not fully understood, and remain one of the key questions in stellar astrophysics. We use a new method to study the extended atmospheres of these cold stars, exploring the effect of a stellar wind for both a simple radiative equilibrium model and a semi-empirical model that accounts for a chromospheric temperature structure. We then can compute the intensities, fluxes and visibilities matching the observations for the different instruments at the Very Large Telescope Interferometer (VLTI). Specifically, when comparing with the atmospheric structure of HD 95687 based on published VLTI/AMBER data, we find that our model can accurately match these observations in the K-band, showing the enormous potential of this methodology to reproduce extended atmospheres of RSGs.