A single component, two-phase lattice Boltzmann model based on the Shan-Chen pseudopotential model is coupled to a continuum-based thermal energy solver. The model is verified using the Stefan problem and Nusselt's falling film. We then use the model to simulate 2D drop-wise condensation of a saturated vapor on hydrophobic structured surfaces. We report the normalized condensed mass and condensation rate as we vary the spacing between structures, numerical interface thickness, and structure topology. For a non-dimensional spacing of s = 6.4, a primary droplet engulfs each post after a non-dimensional thermal diffusion time of t* approximate to 1.1 (square), t* approximate to 0.59 (semi-circular), and t* approximate to 2.38 (equilateral). The growth of this thermally resistant primary droplet is fed by coalescing satellite droplets characterized by low heat transfer resistance. These small satellite droplets continuously nucleate, grow and merge into the primary droplet resulting in condensation rates four to seven times greater than the film-wise condensation rate. These small droplets only appear to form when the ratio of numerical interface thickness w to structure length L is sufficiently small (w/L < 0.1). (C) 2019 Elsevier Ltd. All rights reserved.