The construction of fast reliable low-dimensional models is important for monitoring and control of ventilation applications. We employ a discrete Green’s function approach to derive a linear low-dimensional ventilation model directly from the governing equations for indoor ventilation (i.e., the Navier–Stokes equations supplemented with a transport equation for indoor-pollutant concentration). It is shown that the flow equations decouple from the concentration equation when the ratio α of air-mass-flow rate to pollutant-mass-flow rate increases to infinity. A low-dimensional discrete representation of the Green’s function of the concentration equation can then be constructed, based on either numerical simulations or experiments. This serves as a linear model that allows for the reconstruction of concentration fields resulting from any type of pollutant-source distribution. We employ a suite of Reynolds-averaged Navier–Stokes (RANS) simulations to illustrate the methodology. We focus on a simple benchmark ventilation case under constant-density conditions. Discrete linear ventilation models for the concentration are then derived and compared with coupled RANS simulations. An analysis of errors in the discrete linear model is presented: Dependence of the error on the (low-dimensional) resolution in the discrete model is quantified, and errors introduced by too low values of α are also investigated.