Parametrization and Cartesian representation ...
Document type :
Article dans une revue scientifique: Article original
Title :
Parametrization and Cartesian representation techniques for robust resolution of chemical equilibria
Author(s) :
Jonval, Maxime [Auteur correspondant]
Reliable numerical approximations of dissipative systems [RAPSODI]
IFP Energies nouvelles [IFPEN]
Ben Gharbia, Ibtihel [Auteur correspondant]
IFP Energies nouvelles [IFPEN]
Cancès, Clément [Auteur correspondant]
Reliable numerical approximations of dissipative systems [RAPSODI]
Faney, Thibault [Auteur correspondant]
IFP Energies nouvelles [IFPEN]
Tran, Quang Huy [Auteur correspondant]
IFP Energies nouvelles [IFPEN]
Reliable numerical approximations of dissipative systems [RAPSODI]
IFP Energies nouvelles [IFPEN]
Ben Gharbia, Ibtihel [Auteur correspondant]
IFP Energies nouvelles [IFPEN]
Cancès, Clément [Auteur correspondant]
Reliable numerical approximations of dissipative systems [RAPSODI]
Faney, Thibault [Auteur correspondant]
IFP Energies nouvelles [IFPEN]
Tran, Quang Huy [Auteur correspondant]
IFP Energies nouvelles [IFPEN]
Journal title :
Journal of Computational Physics
Pages :
113596
Publisher :
Elsevier
Publication date :
2025-02-01
ISSN :
0021-9991
English keyword(s) :
Chemical equilibria
Newton's method
Parametrization
Cartesian representation
Newton's method
Parametrization
Cartesian representation
HAL domain(s) :
Mathématiques [math]/Analyse numérique [math.NA]
Chimie
Chimie
English abstract : [en]
Chemical equilibria computations, especially those with vanishing species in the aqueous phase, lead to nonlinear systems that are difficult to solve due to gradient blow up. Instead of the commonly used ad hoc treatments, ...
Show more >Chemical equilibria computations, especially those with vanishing species in the aqueous phase, lead to nonlinear systems that are difficult to solve due to gradient blow up. Instead of the commonly used ad hoc treatments, we propose two reformulations of the single-phase chemical equilibrium problem which are in line with the spirit of preconditioning but whose actual aims are to guarantee a better stability of Newton's method. The first reformulation is a parametrization of the graph linking species mole fractions to their chemical potentials. The second is based on an augmented system where this relationship is relaxed for the iterates by means of a Cartesian representation. We theoretically prove the local quadratic convergence of Newton's method for both reformulations. From a numerical point of view, we demonstrate that the two techniques are accurate, allowing to compute equilibria with chemical species having very low concentrations. Moreover, the robustness of our methods combined with a globalization strategy is superior to that of the literature.Show less >
Show more >Chemical equilibria computations, especially those with vanishing species in the aqueous phase, lead to nonlinear systems that are difficult to solve due to gradient blow up. Instead of the commonly used ad hoc treatments, we propose two reformulations of the single-phase chemical equilibrium problem which are in line with the spirit of preconditioning but whose actual aims are to guarantee a better stability of Newton's method. The first reformulation is a parametrization of the graph linking species mole fractions to their chemical potentials. The second is based on an augmented system where this relationship is relaxed for the iterates by means of a Cartesian representation. We theoretically prove the local quadratic convergence of Newton's method for both reformulations. From a numerical point of view, we demonstrate that the two techniques are accurate, allowing to compute equilibria with chemical species having very low concentrations. Moreover, the robustness of our methods combined with a globalization strategy is superior to that of the literature.Show less >
Language :
Anglais
Peer reviewed article :
Oui
Audience :
Internationale
Popular science :
Non
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