Computational investigations of combustion have been useful in understanding the phenomena governing internal combustion engines to help make them more efficient and less polluting. However, the nonlinearity of chemistry source terms limits large-scale CFD simulations to simple chemistry (no more than 50 species), in contrast to the complicated chemical mechanisms being developed by chemists (ranging from hundreds to thousands of species). In order to model accurately the formation of soot and pollutants in engines, this detailed chemistry must be modeled faithfully with computationally efficient approximations that can be incorporated into large-scale CFD simulations without making their computational costs prohibitive. To faithfully approximate the chemistry efficiently, a variety of model reduction methods, such as reaction elimination, simultaneous reaction and species elimination, directed relation graphs, pure species elimination, and projection-based model reduction have been developed. Special attention has been paid to developing methods with error control, understanding the common mathematical structure of different methods, and relating the error control in these methods to the error in the solution of a reduced model. An overview of recent work will be presented, demonstrating the extent to which models can be reduced at given error tolerances, and showing the tradeoff between the computational expense of model reduction and the computational savings obtained from reduced models. These results illustrate that it is possible to incorporate error control into model reduction methods in combustion without prohibitive computational costs, making it possible to use more detailed chemistry in CFD simulations.
