Adaptive hierarchical construction of Reaction-Diffusion Manifolds for simplified chemical kinetics

The manifolds based model reduction strategy has become a key approach in detailed modelling and simulations of reacting flows. The methodology has very important advantages over other reduction strategies, namely, a very low dimensionality of the resulting reduced model and a high accuracy of the results. In the present study the problem of model reduction of premixed combustion systems is discussed. The method of Reaction-Diffusion Manifolds (REDIM) is further developed to handle generically high dimensional reduced models. Three main problems of manifold based model reduction strategies were in the focus of the study: the generation of manifolds of arbitrary dimension, the definition of the manifold domain for the specific problem and the independence of a priori information from detailed calculations. Hierarchical structure of the manifold with respect to dimensionality together with a natural geometrical observation that the manifold should degenerate on its boundary allow us to overcome the first two problems for this type of model reduction. A simple but meaningful example of a syngas/air system is used to illustrate the insensitivity of the reduced model with respect to detailed system information, i.e., detailed system gradients. To validate the reduced model the relaxation process of perturbed flame profiles is investigated. The results of comparison of the reduced and detailed transient solutions show a great potential for the suggested methodology to handle the premixed combustion systems.