Approximate non-linear lumping in systems with time-scale separation

2 Approximate non-linear lumping in systems with time-scale separation 

Finding canonical forms for each of the A s, is an easier task than for any general form A. A technique has been developed at Princeton [189-191] for finding such canonical forms using an algebraic method in nonlinear perturbation theory. For the application of this technique the leading operator Aq must be chosen to be in canonical form. The basic approach is then to find a non-linear transformation C such that the resultant operator. 

Direct comparisons can be made with the Schur transformation in the linear case. Other techniques based on the use of algebraic sets for the approximation of non-linear inertial manifolds have also been developed [192] but have not yet been applied in combustion systems. 

3 Application of approximate non-linear lumping to the hydrogen oxidation example 

In this section we will again use the hydrogen oxidation scheme to show how approximate lumping methods can lead to improved solutions over the QSSA, but to a more complex form for the reduced scheme. For the illustration of this point we will use the core set of reactions used in the QSSA section which represent the most basic ignition system. 

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