Adaptive Simplification of Complex Systems: A Review of the Relaxation-Redistribution Approach

We present a review of a recently introduced methodology for reducing complexity of large dissipative systems such as detailed reaction mechanisms of combustion and biochemical reactions whose dynamics is characterized by a hierarchy of slow invariant manifolds. Accurate reduced description is achieved by construction of slow invariant manifolds with an embarrassingly simple implementation in any dimension. The method is validated with the auto-ignition of the hydrogen-air mixture where a reduction to a cascade of slow invariant manifolds is observed.