Труды сотрудников ИВМ СО РАН

[Text] : статья / E. Chiavazzo, I. V. Karlin // Journal of Computational Physics. - 2008. - Vol. 227, Iss. 11. - p. 5535–5560DOI 10.1016/j.jcp.2008.02.006 . -
Аннотация: The method of invariant grid (MIG) is an iterative procedure for model reduction in chemical kinetics which is based on the notion of Slow Invariant Manifold (SIM) [A.N. Gorban, I.V. Karlin, Method of invariant manifold for chemical kinetics, Chem. Eng. Sci. 58 (2003) 4751–4768; E. Chiavazzo, A.N. Gorban, I.V. Karlin, Comparison of invariant manifolds for model reduction in chemical kinetics, Commun. Comput. Phys. 2(5) (2007) 964–992; A.N. Gorban, I.V. Karlin, A.Y. Zinovyev, Invariant grids for reaction kinetics, Physica A 333 (2004) 106–154; A.N. Gorban, I.V. Karlin, Invariant Manifolds for Physical and Chemical Kinetics, Lecture Notes Physics 660, Springer, Berlin Heidelberg, 2005, doi: 10.1007/b98103]. Important role, in that method, is played by the initial grid which, once refined, gives a description of the invariant manifold: the invariant grid. A convenient way to get a first approximation of the SIM is given by the spectral quasi-equilibrium manifold (SQEM) [A.N. Gorban, I.V. Karlin, Method of invariant manifold for chemical kinetics, Chem. Eng. Sci. 58 (2003) 4751–4768; E. Chiavazzo, A.N. Gorban, I.V. Karlin, Comparison of invariant manifolds for model reduction in chemical kinetics, Commun. Comput. Phys. 2(5) (2007) 964–992]. In the present paper, a flexible numerical method to construct the discrete analog of a quasi-equilibrium manifold, in any dimension, is presented. That object is named quasi-equilibrium grid (QEG), while the procedure quasi-equilibrium grid algorithm (QEGA). Extensions of the QEM notion are also suggested. The QEGA is a numerical tool which can be used to find a grid-based approximation for the locus of minima of a convex function under some linear constraints. The method is validated by construction of one and two-dimensional grids for a model of hydrogen oxidation reaction.

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Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

Доп.точки доступа:
Karlin, I.V.; Карлин, Илья Вениаминович

[Text] : статья / E. Chiavazzo [et al.] // Proceedings of the Combustion Institute. - 2008. - Vol. 32, Iss. 1. - p. 519–526DOI 10.1016/j.proci.2008.05.014 . -
Аннотация: The Method of Invariant Grid (MIG) is a model reduction technique based on the concept of slow invariant manifold (SIM). The MIG approximates the SIM by a set of nodes in the concentration space (invariant grid). In the present work, the MIG is applied to a realistic combustion system: an adiabatic constant volume reactor with H2–air at stoichiometric proportions. By considering the thermodynamic Lyapunov function of the detailed kinetic system, the notion of the quasi-equilibrium manifold (QEM) is adopted as an initial approximation to the SIM. One- and two-dimensional discrete approximations of the QEM (quasi-equilibrium grids) are constructed and refined via MIG to obtain the corresponding invariant grids. The invariant grids are tabulated and used to integrate the reduced system. Excellent agreement between the reduced and detailed kinetics is demonstrated.

Полный текст на сайте правообладателя

Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44

Доп.точки доступа:
Chiavazzo, Eliodoro; Karlin, I.V.; Карлин, Илья Вениаминович; Frouzakisa, Christos; Boulouchos, Konstantinos

[Text] : статья / E. Chiavazzo [et al.] // International Journal of Numerical Methods for Heat & Fluid Flow. - 2011. - Vol. 21, Iss. 5. - p. 494-517, DOI 10.1108/09615531111135792 . - ISSN 0961-5539
Аннотация: Purpose – The paper aims to be a first step toward the efficient, yet accurate, solution of detailed combustion fields using the lattice Boltzmann (LB) method, where applications are still limited due to both the stiffness of the governing equations and the large amount of fields to solve. Design/methodology/approach – The suggested methodology for model reduction is developed in the setting of slow invariant manifold construction, including details of the while. The simplest LB equation is used in order to work out the procedure of coupling of the reduced model with the flow solver. Findings – The proposed method is validated with the 2D simulation of a premixed laminar flame in the hydrogen-air mixture, where a remarkable computational speedup and memory saving are demonstrated. Research limitations/implications – Because of the chosen detailed LB model, the flow field may be described with unsatisfactory accuracy: this motivates further investigation in this direction in the near future. Practical implications – A new framework of simulation of reactive flows is available, based on a coupling between accurate reduced reaction mechanism and the LB representation of the flow phenomena. Hence, the paper includes implications on how to perform accurate reactive flow simulations at a fraction of the cost required in the detailed model. Originality/value – This paper meets an increasing need to have efficient and accurate numerical tools for modelling complex phenomena, such as pollutant formation during combustion.


Доп.точки доступа:
Chiavazzo, Eliodoro; Karlin, I.V.; Карлин, Илья Вениаминович; Gorban, A.N.; Горбань, Александр Николаевич; Boulouchos, Konstantinos