A scale-resolving CFD modelling approach allowing an in-depth analysis of hydrodynamics and heat transfer in irregular, highly porous structures is presented. It has been developed for experimentally well-characterized solid sponges, also often referred to as open-celled foams, but can be applied to similar structures as well. Due to computational cost limitations, it is necessary to restrict the scale-resolved CFD calculations to adequately sized and shaped representative elementary volumes (REVs) of the porous structure only. A special multi-zone approach has been developed to still allow the specification of realistic hydrodynamic and thermal boundary conditions. It also considers the influence of the REV's real surrounding if inserted for example into a larger pipe or reactor. It relies on the coupling of the scale resolved REV calculations with so-called porous 'embedding zones' which are being modelled as homogeneous porous media having equivalent effective properties. Two different heat transfer models are presented which allow both the separate analysis of convective fluid heat transfer only and the coupled analysis of conjugate fluid-solid heat transfer. Systematic parameter variations (superficial velocity and solid heat conductivity) have been carried out to work out the fluid and solid heat transfer contributions. Finally, results derived for the integral quantities pressure drop Delta p and volumetric heat transfer coefficient alpha(v,F-S) are compared to the validation data available from literature and show good agreement. (C) 2016 Elsevier Ltd. All rights reserved.