Implementation problems of manifolds-based model reduction and their generic solution

During the last decades, tabulated chemistry approaches, like manifold-based concepts to implement model reduction, have become a widespread, promising and accurate method to take chemical reactions into account in computing reacting flows. However, there is a number of crucial issues concerning the generation and implementation of the tabulated chemistry approaches. These concern the way manifolds of the arbitrary dimension are generated, parametrised (i.e. tabulated) preserving fast/slow decomposition and implemented rigorously by the formulation of a reduced model in a coordinate independent manner.

This study discusses these problems in detail and suggests generic solutions based on the Reaction–Diffusion Manifolds (REDIM) method. A REDIM tabulated chemistry concept obtained by using the hierarchical nature of the invariant slow system manifolds is presented. Numerical aspects of the implementation are in the focus of the paper. It is shown how the concept is implemented to overcome most problems without a-priori knowledge of the considered system behaviour. As a basic example for discussion and illustration synthesis, gas/air combustion in premixed, freely propagating flames is used.