The invariant constrained equilibrium edge preimage curve method for the dimension reduction of chemical kinetics

This work addresses the construction and use of low-dimensional invariant manifolds to simplify complex chemical kinetics. Typically, chemical kinetic systems have a wide range of time scales. As a consequence, reaction trajectories rapidly approach a hierarchy of attracting manifolds of decreasing dimension in the full composition space. In previous research, several different methods have been proposed to identify these low-dimensional attracting manifolds. Here we propose a new method based on an invariant constrained equilibrium edge (ICE) manifold. This manifold (of dimension nr) is generated by the reaction trajectories emanating from its (nr-1)-dimensional edge, on which the composition is in a constrained equilibrium state. A reasonable choice of the nr represented variables (e.g., nr "major" species) ensures that there exists a unique point on the ICE manifold corresponding to each realizable value of the represented variables. The process of identifying this point is referred to as species reconstruction. A second contribution of this work is a local method of species reconstruction, called ICE-PIC, which is based on the ICE manifold and uses preimage curves (PICs). The ICE-PIC method is local in the sense that species reconstruction can be performed without generating the whole of the manifold (or a significant portion thereof). The ICE-PIC method is the first approach that locally determines points on a low-dimensional invariant manifold, and its application to high-dimensional chemical systems is straightforward. The "inputs" to the method are the detailed kinetic mechanism and the chosen reduced representation (e.g., some major species). The ICE-PIC method is illustrated and demonstrated using an idealized H2O system with six chemical species. It is then tested and compared to three other dimension-reduction methods for the test case of a one-dimensional premixed laminar flame of stoichiometric hydrogen/air, which is described by a detailed mechanism containing nine species and 21 reactions. It is shown that the error incurred by the ICE-PIC method with four represented species is small across the whole flame, even in the low temperature region.