Order reduction of a non-Lipschitzian model of monodisperse spray ignition

Sazhin, S.S., Shchepakina, E. and Sobolev, V. (2010) Order reduction of a non-Lipschitzian model of monodisperse spray ignition Mathematical and Computer Modelling, 52 (3-4). pp. 529-537. ISSN 0895-7177

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Abstract

It is pointed out that the order reduction of singular perturbed systems with non-Lipschitzian nonlinearities can be performed, using the new concept of positively (negatively) invariant manifolds, if the five assumptions of the Tikhonov theorem are satisfied. Examples when these assumptions are satisfied and not satisfied are presented and discussed. The previously derived singularly perturbed system of three equations (droplet radii, gas temperature and fuel vapour concentration), describing evaporation and ignition of monodisperse fuel sprays, are shown to satisfy all five assumptions of the Tikhonov theorem. This allows us to reduce this system to a system of two equations describing the gas temperature and fuel concentration when the droplet evaporation process has been completed.

Item Type: Journal article
Uncontrolled Keywords: Monodisperse spray; ignition; singular perturbations; non-Lipschitzian equations; positively (negatively) invariant manifolds
Subjects: H000 Engineering > H300 Mechanical Engineering > H330 Automotive Engineering
DOI (a stable link to the resource): 10.1016/j.mcm.2010.03.051
Faculties: Faculty of Science and Engineering > School of Computing, Engineering and Mathematics > Engineering and Product Design Research > Automotive Engineering
Depositing User: editor engineering
Date Deposited: 11 Mar 2011 10:03
Last Modified: 20 Apr 2012 09:09
URI: http://eprints.brighton.ac.uk/id/eprint/8337

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