  Sensitivity analysis with forced optimally time dependent (f-OTD) modes is
introduced and its application for skeletal model reduction is demonstrated.
f-OTD expands the sensitivity coefficient matrix into a lowdimensional, time
dependent, orthonormal basis which captures directions of the phase space
associated with most dominant sensitivities. These directions highlight the
instantaneous active species and reaction paths. Evolution equations for the
orthonormal basis and the projections of sensitivity matrix onto the basis are
derived, and the application of f-OTD for skeletal reduction is described. In
this framework, the sensitivity matrix is modeled, stored in a factorized
manner, and never reconstructed at any time during the calculations. For
demonstration purposes, sensitivity analysis is conducted of constant pressure
ethylene-air burning in a zero-dimensional reactor and new skeletal models are
generated. The flame speed, the ignition delay, and the extinction curve of
resulted models are compared against some of the existing skeletal models. The
results demonstrate the ability of f-OTD approach to eliminate unimportant
reactions and species in a systematic, efficient and accurate manner.
