Thanks to strong heat recirculation, submerged combustion within porous media presents unique technological features such as broadened flammability limits and extended power range. The associated possibility to burn ultra-lean mixtures with minimal CO/NOx emissions makes porous media combustion a potential alternative in the industry, for instance in domestic heat generation or clean aviation where low pollutant emissions and robust operability are of paramount importance. However, even though this combustion mode has been studied for decades, there remains many open questions regarding the intertwined flame structure and the validity of associated low-order modelling. To date, volume-averaged models are mostly based upon ad hoc hypotheses and still present large discrepancies with experiments. Aiming to chal- lenge and strengthen these models, the present work presents analytical and numerical studies of the volume-averaged equations, followed by 3D direct pore-level simulations of methane-air and hydrogen-air combustion. Chapters 1 and 2 provide a critical review of concepts associated to flows and flames within porous media, with a focus on non-adiabatic combustion and macroscopic effective characteriza- tion. A classification of gaseous flames in terms of the thermal Péclet number is proposed, and the upscaling procedure on the pointwise equations is presented. Chapter 3 presents asymptotic results based on the volume-averaged equations, and the proposed theoretical framework un- veils the first fully-explicit formulae for flame speed in infinite and finite-length porous burners. Multi-layered burners are also considered theoretically for the first time, and the important con- cept of contact resistance between two stacked porous plates is underlined. Chapter 4 proposes a general classification of porous media combustion in three distinct regimes for increasing inter- phase heat transfer, only based on two reduced parameters, in order to reconcile the literature frameworks of local thermal equilibrium (LTE) and non-equilibrium (LTNE). Chapter 5, 6 and 7 present 3D pore-level direct numerical simulations of flames within porous media using complex kinetics, for various structural topologies and pore sizes. As a major technical hurdle encountered during the thesis, the meshing workflow from X-ray tomography to conformal computational mesh is given for practical use in the community. These DNS unveil the internal flame structure of methane-air and hydrogen-air flames within typical porous burners, and it is shown that when the pore size is larger than the flame thickness, sharp and locally- anchored flame fronts are observed. These local discontinuities related to the strongly non-linear reaction rates are shown to be in direct violation of the classical volume-averaged hypotheses. This demonstrates that new volume-averaged models are required, and accordingly a closure for reaction rates based upon phenomenology and observations in the 3D DNS is proposed. Eventually, the pore-level specificities of hydrogen combustion at pore scale are described
