eprintid: 7352
rev_number: 9
eprint_status: archive
userid: 1
dir: disk0/00/00/73/52
datestamp: 2007-05-11 09:54:07
lastmod: 2015-04-22 06:52:16
status_changed: 2012-08-14 15:21:39
type: preprint
metadata_visibility: show
creators_name: Reinhardt, Volkmar
creators_name: Winckler, Miriam
creators_name: Lebiedz, Dirk
title: Approximation of slow attracting manifolds in chemical kinetics by trajectory-based optimization approaches
ispublished: pub
subjects: ddc-510
divisions: i-708000
keywords: Nonlinear model reduction , optimization
cterms_swd: TOMP
abstract: Many common kinetic model reduction approaches are explicitly based on inherent multiple time scales and often assume and directly exploit a clear time scale separation into fast and slow reaction processes. They approximate the system dynamics with a dimension-reduced model after eliminating the fast modes by enslaving them to the slow ones. The corresponding restrictive assumption of full relaxation of fast modes often renders the resulting approximation of slow attracting manifolds inaccurate as a representation of the reduced model and makes the numerical solution of the nonlinear “reduction equations” particularly difficult in many cases where the gap in intrinsic time scales is not large enough. We demonstrate that trajectory optimization approaches can avoid such severe restrictions by computing numerical solutions that correspond to “maximally relaxed” dynamical modes in a suitable sense. We present a framework of trajectory-based optimization for model reduction in chemical kinetics and a general class of reduction criteria characterizing the relaxation of chemical forces along reaction trajectories. These criteria can be motivated geometrically exploiting ideas from differential geometry and fundamental physics and turn out to be highly successful in example applications. Within this framework, we provide results for the computational approximation of slow attracting low-dimensional manifolds in terms of families of optimal trajectories for a six-component hydrogen combustion mechanism.
abstract_translated_lang: eng
date: 2007
date_type: published
id_scheme: DOI
id_number: 10.11588/heidok.00007352
portal_cluster_id: p-iwrpp
portal_order: 07352
ppn_swb: 1646175689
own_urn: urn:nbn:de:bsz:16-opus-73522
language: eng
bibsort: REINHARDTVAPPROXIMAT2007
full_text_status: public
series: IWR-Preprints
citation:   Reinhardt, Volkmar ; Winckler, Miriam ; Lebiedz, Dirk  (2007) Approximation of slow attracting manifolds in chemical kinetics by trajectory-based optimization approaches.  [Preprint]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/7352/1/modelred_optimization.pdf