: Increasing combustion efficiency saves huge amounts of fuel, decreases combustion pollution, and conserves the living environment. Among all the ways that are proposed for increasing combustion efficiency, utilizing porous media in the combustion zone is one of the best. High developing inner surface and turbulence structure of the gas flow through porous media make combustion totally different form that of free flame combustion. Due to the complexity of the porous structure and high temperature value of the combustion product, installing experimental devices to investigate the effects of the porous media on fluid behavior in the combustion zone is difficult and expensive. In this situation numerical methods are utilized to investigate the flow behavior for combustion in the porous media. Like in many other fields of fluid dynamics, computational fluid dynamics (CFD) has become an important part of combustion research. Although the speed and storage capacity of modern computers increases continuously, it is still impossible to employ models that use detailed chemistry for the simulation of combustion in practical furnaces. Especially the models for turbulent flames are tremendously complicated due to the large range of time and length scales involved. Nowadays, numerical simulations of one-dimensional laminar flames with detailed chemistry and traort models are often used in combustion research. Nevertheless, the computation time for multi-dimensional laminar flame models prohibits the simulation of flames in complex geometries or an investigation of the influence of different parameters. Therefore, several methods to simplify the description of the reaction kinetics have been developed during the last decades. The main part of these methods is based on the assumption that most chemical processes in a flame have a much smaller time scale than the flow time scale. These assumptions, however, give poor approximations in the ’colder’ regions of a flame, in which traort processes are also important. In this thesis a new method is presented, which can be considered as a combination of two existing approaches to speed up flame calculations, i.e. the flamelet and manifold approach. This new method, referred to as the Flamelet-Generated Manifold (FGM) method, shares the idea with flamelet approaches that a multi-dimensional flame may be considered as a set of one-dimensional flames. The thermo-chemical variables are stored in a database, which can be used in subsequent flame simulations. During the flame simulation conservation equations have to be solved for the controlling variables only. Since the major parts of convection and diffusion processes are present in one dimensional flamelets, the FGM method is more accurate in the ’colder’ zones of premixed flames than reduction methods based on local chemical equilibria. Test results of one- and two-dimensional methane/air flames show that detailed chemistry computations are reproduced very well by using a FGM with only one progress variable apart from the enthalpy to account for energy losses. Due to the application of the FGM method, the computation time has been reduced by a factor of 50 in one-dimensional flames demonstrating the enormous potential of the method. For two-dimensional flames the computational gain is even larger. Simulations were separately performed by using the aforementioned progress variables and the prediction of the flame front were compared . Submerged flames within porous media simulated in three burners with different geometry and porous materials. Each of these burners was simulated with different models for volumetric heat transfer coefficient between the two phases which shows that the use of different models for heat transfer has a significant impact on the results. Then a burner with different conduction heat transfer coefficients of solid matrix was simulated. Key Words—Premixed Combustion , Porous Media, submerged Flame, Flamelet Generated Manifold, reducing computational costs.