In numerical simulations of combustion processes, the use of dimension reduction to simplify the description of the chemical system has the advantage of reducing the computational cost, but it is important also to retain accuracy and adequate detail. In current research, dimension reduction of combustion chemistry is performed by using the ICE-PIC method. The ICE-PIC method is developed based on three major ingredients: constrained equilibrium; trajectory-generated manifolds; and, the pre-image curve method. The low-dimensional manifold identified, the ICE manifold, is invariant, continuous and piecewise smooth. The ICE-PIC method achieves local species reconstruction based on the constrained-equilibrium pre-image curve. In comparison to other existing methods such as QSSA, RCCE and ILDM, this method is the first approach that locally determines compositions on a low-dimensional invariant manifold.

The accuracy of the ICE-PIC method has been examined in autoignition and in one-dimensional laminar flames of hydrogen/air and methane/air mixtures. Studies demonstrate that the local errors incurred by ICE-PIC (e.g., the errors in the reconstructed composition) are well controlled. The capability of the ICE-PIC method for the reduced description of reactive flows is demonstrated through the calculation of the oxidation of CO/H2 in a CSTR. The reduced description provided by the ICE-PIC method is capable of quantitatively reproducing the complex dynamics.

The final goal is to develop an efficient and accurate algorithm - In Situ Adaptive Tabulation with Dimension Reduction (the ICE-PIC method) to incorporate detailed chemistry in turbulent combustion simulations.