The extension of the ILDM concept to reaction–diffusion manifolds

Abstract

In the present work, the method of simplifying chemical kinetics based on Intrinsic Low-Dimensional Manifolds (ILDMs) is modified to deal with the coupling of reaction and diffusion processes. Several problems of the ILDM method are overcome by a relaxation to an invariant system manifold (Reaction–Diffusion Manifold – REDIM). This relaxation process is governed by a multidimensional parabolic partial differential equation system, where, as an initial solution, an extended ILDM is used. Furthermore, a method for the solution and tabulation of the manifold is proposed in terms of generalized coordinates, with a subsequent procedure for the integration of the reduced system on the found manifold. This modification of the ILDM significantly improves the performance of the concept and allows us to extend its area of applicability. Illustrative comparative calculations of detailed and reduced models of flat laminar flames verify the approach.

Keywords:

• Chemical kinetics
• Dimension reduction
• ILDM
• Invariant manifolds
• Laminar flame

Acknowledgments

Financial support by the DFG is gratefully acknowledged. V.B. wishes to thank the Max Planck Society for the financial support under the Minerva Fellowship Program.