Abstract
A wide range of dynamic models, including those of heating, evaporation
and ignition processes in fuel sprays, is characterised by large differences
in the rates of change of variables. Invariant manifold theory is an effective
technique for investigation of these systems. In constructing the asymptotic
expansions of slow invariant manifolds it is commonly assumed that a limiting
algebraic equation allows one to find a slow surface explicitly. This is not
always possible due to the fact that the degenerate equation for this surface
(small parameter equal to zero) is either a high degree polynomial or transcendental. In many problems, however, the slow surface can be described in
a parametric form. In this case, the slow invariant manifold can be found in
parametric form using asymptotic expansions. If this is not possible, it is necessary to use an implicit presentation of the slow surface and obtain asymptotic representations for the slow invariant manifold in an implicit form. The results of development of the mathematical theory of these approaches and the applications of this theory to some examples related to modelling combustion
processes, including those in sprays, are presented.
and ignition processes in fuel sprays, is characterised by large differences
in the rates of change of variables. Invariant manifold theory is an effective
technique for investigation of these systems. In constructing the asymptotic
expansions of slow invariant manifolds it is commonly assumed that a limiting
algebraic equation allows one to find a slow surface explicitly. This is not
always possible due to the fact that the degenerate equation for this surface
(small parameter equal to zero) is either a high degree polynomial or transcendental. In many problems, however, the slow surface can be described in
a parametric form. In this case, the slow invariant manifold can be found in
parametric form using asymptotic expansions. If this is not possible, it is necessary to use an implicit presentation of the slow surface and obtain asymptotic representations for the slow invariant manifold in an implicit form. The results of development of the mathematical theory of these approaches and the applications of this theory to some examples related to modelling combustion
processes, including those in sprays, are presented.
Original language  English 

Pages (fromto)  117 
Journal  Journal of Engineering Mathematics 
Volume  114 
DOIs  
Publication status  Published  7 Dec 2018 
Bibliographical note
This is a postpeerreview, precopyedit version of an article published in Journal of Engineering Mathematics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s1066501899764Keywords
 Invariant manifold System order reduction
 spray ignition
 spray combustion
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Sergei Sazhin
 School of Arch, Tech and Eng  Professor of Thermal Physics
 Centre for Precision Health and Translational Medicine
 Advanced Engineering Centre
Person: Academic