Ceccato, Alessandro (2014) Metodi computazionali per la costruzione di superfici Â€ÂśSlow ManifoldÂ€Âť nella riduzione di dimensionalita' in cinetica chimica. [Magistrali biennali]
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The present project fits in the context of devising theoretical-computational strategies aimed to simplify the description of chemical kinetics when many species are involved in the reaction of interest. Here we focus on well-stirred reacting systems in isothermal conditions, so that the dynamical variables are the volumetric concentrations of the species. It is assumed that the complex reaction owns a kinetic scheme made of known elementary steps (or, similarly, a reaction network is formed by elementary reactions) to which the Mass-Action Law is applicable to construct the system of differential equations governing the time evolution. The main goal of this work is to achieve the simplification of the kinetics description via the construction of hypersurfaces called Slow Manifolds (SMs) in the Literature. Since a SM has lower dimension than the number of chemical species involved in the reaction, and since the slow part of the evolution is found to take place in the neighborhood of the SM (after an initial transient), the identification of these surfaces may allow an efficient simplification in terms of reduction of the number of relevant dynamical variables. In the first part of the thesis we review the state of the art of the methods available in Literature to construct the SMs. Then we stand on a formal and objective mathematical definition of the SM recently proposed [P. Nicolini and D. Frezzato, J. Chem. Phys. 138, 234101 (2013); ibid., J. Chem. Phys. 138, 234102 (2013)], and develop computational strategies to â€śtranslateâ€ť it in the numerical practice. Codes in programming language FORTRAN77 have been created to implement these strategies and to test their efficiency both on low-dimensional model kinetic schemes, and on a simplified scheme for hydrogen combustion widely taken as benchmark in the Literature. Although the methods developed by us are based on a rigorous definition of Slow Manifold, and the results for the model-schemes are satisfactory, the tests on the hydrogen combustion scheme reveal that the choice of some work-parameters (required to perform the calculations) may largely affect the outcomes. In this respect, the algorithmic translations of the formal definition of Slow Manifold is not yet fully satisfactory. In the final chapter we argue some possible improvements of the methods, namely the exploitation of data clustering algorithms to exclude spurious solutions, the inclusion of the temperature amongst the dynamical variables, and the consideration of non-elementary reactions.
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