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The theory of inertial manifolds (IM) is used to develop reduced-order modelsof turbulent combustion. In this approach, the dynamics of the system aretracked in a low-dimensional manifold determined in-situ without invokinglaminar flame structures or statistical assumptions about the underlyingturbulent flow. The primary concept in approximate IM (AIM) is that slowdominant dynamical behavior of the system is confined to a low-dimensionmanifold, and fast dynamics respond to the dynamics on the IM instantaneously.Decomposition of slow/fast dynamics and formulation of an AIM is accomplishedby only exploiting the governing equations. Direct numerical simulations (DNS)of initially non-premixed fuel-air mixtures developing in forced isotropicturbulence have been carried out to investigate the proposed model. Reactionrate parameters are varied to allow for varying levels of extinction andreignition. The AIM performance in capturing different flame behaviors isassessed both a priori and a posteriori. It is shown that AIM captures thedynamics of the flames including extinction and reignition. Moreover, AIMprovides scalar dissipation rate, mixing time for reactive scalars, andclosures for nonlinear terms without any additional modeling. The AIMformulation is found promising, and provides a new approach to modelingturbulent combustion.

Using approximate inertial manifold approach to model turbulent non-premixed combustion