A modern approach to model reduction in chemical kinetics is often based on the notion of slow invariant manifold.The goal of this paper is to give a comparison of various methods of construction of slow invariant man...A modern approach to model reduction in chemical kinetics is often based on the notion of slow invariant manifold.The goal of this paper is to give a comparison of various methods of construction of slow invariant manifolds using a simple Michaelis-Menten catalytic reaction.We explore a recently introduced Method of Invariant Grids(MIG)for iteratively solving the invariance equation.Various initial approximations for the grid are considered such as Quasi Equilibrium Manifold,Spectral Quasi Equilibrium Manifold,Intrinsic Low Dimensional Manifold and Symmetric Entropic Intrinsic Low Dimensional Manifold.Slow invariant manifold was also computed using the Computational Singular Perturbation(CSP)method.A comparison between MIG and CSP is also reported.展开更多
In the present work,we develop in detail the process leading to reduction of models in chemical kinetics when using the Method of Invariant Grids(MIG).To this end,reduced models(invariant grids)are obtained by refinin...In the present work,we develop in detail the process leading to reduction of models in chemical kinetics when using the Method of Invariant Grids(MIG).To this end,reduced models(invariant grids)are obtained by refining initial approximations of slow invariant manifolds,and used for integrating smaller and less stiff systems of equations capable to recover the detailed description with high accuracy.Moreover,we clarify the role played by thermodynamics in model reduction,and carry out a comparison between detailed and reduced solutions for a model hydrogen oxidation reaction.展开更多
基金supported by SNF,Project 200021-107885/1(E.C.)and by BFE,Project 100862(I.V.K.)。
文摘A modern approach to model reduction in chemical kinetics is often based on the notion of slow invariant manifold.The goal of this paper is to give a comparison of various methods of construction of slow invariant manifolds using a simple Michaelis-Menten catalytic reaction.We explore a recently introduced Method of Invariant Grids(MIG)for iteratively solving the invariance equation.Various initial approximations for the grid are considered such as Quasi Equilibrium Manifold,Spectral Quasi Equilibrium Manifold,Intrinsic Low Dimensional Manifold and Symmetric Entropic Intrinsic Low Dimensional Manifold.Slow invariant manifold was also computed using the Computational Singular Perturbation(CSP)method.A comparison between MIG and CSP is also reported.
基金partially supported by SNF(Project 200021-107885/1)(E.C.)CCEMCH(I.V.K.).
文摘In the present work,we develop in detail the process leading to reduction of models in chemical kinetics when using the Method of Invariant Grids(MIG).To this end,reduced models(invariant grids)are obtained by refining initial approximations of slow invariant manifolds,and used for integrating smaller and less stiff systems of equations capable to recover the detailed description with high accuracy.Moreover,we clarify the role played by thermodynamics in model reduction,and carry out a comparison between detailed and reduced solutions for a model hydrogen oxidation reaction.
