New laws and regulations issued to reduce environmental impact together with interests in supersonic engines have imposed the development of newer combustor geometries. It is fundamental to analyze their functioning first of all through numerical simulations. This work aims to study the behavior of different combustors with main focus on innovative configurations and non pre-mixed combustion. Numerical simulations of reacting flows in classical and advanced combustor geometries have been performed. Different conditions have been tested in terms of numerical setups and reaction mechanisms such as use of CH4 and H2 as fuel with air mixture (O2 and N2) for the methane and O2 for gaseous hydrogen.