Compositional gas flow in a heterogeneous porous medium and in the coupled atmospheric boundary layer above the porous medium surface is of interest in many applications, which requires reliable numerical tools for modeling of very complex physical processes. But there are still many important effects which are very often ignored in contemporary models of this flow. One of them is compressibility. So far, no models of non-isothermal compositional compressible gas flow in a porous medium and in the coupled atmospheric boundary layer above its surface has been reported in the literature. Therefore, we propose mathematical and numerical models for the description of the above scenario. In order to assess the reliability of our numerical model, we analyze its convergence by quantitative computational studies. We also present several qualitative computational studies which present the dynamics of the non-isothermal compositional compressible gas flow in free flow–porous medium flow interaction.