Approximation of slow and fast dynamics in multiscale dynamical systems by the linearized Relaxation Redistribution Method
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arXiv
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| Format: | Preprint |
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2011
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| _version_ | 1866914064938041344 |
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| author | Chiavazzo, Eliodoro |
| author_facet | Chiavazzo, Eliodoro |
| contents | In this paper, we introduce a fictitious dynamics for describing the only fast relaxation of a stiff ordinary differential equation (ODE) system towards a stable low-dimensional invariant manifold in the phase-space (slow invariant manifold - SIM). As a result, the demanding problem of constructing SIM of any dimensions is recast into the remarkably simpler task of solving a properly devised ODE system by stiff numerical schemes available in the literature. In the same spirit, a set of equations is elaborated for local construction of the fast subspace, and possible initialization procedures for the above equations are discussed. The implementation to a detailed mechanism for combustion of hydrogen and air has been carried out, while a model with the exact Chapman-Enskog solution of the invariance equation is utilized as a benchmark. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1102_0730 |
| institution | arXiv |
| publishDate | 2011 |
| record_format | arxiv |
| spellingShingle | Approximation of slow and fast dynamics in multiscale dynamical systems by the linearized Relaxation Redistribution Method Chiavazzo, Eliodoro Statistical Mechanics Dynamical Systems In this paper, we introduce a fictitious dynamics for describing the only fast relaxation of a stiff ordinary differential equation (ODE) system towards a stable low-dimensional invariant manifold in the phase-space (slow invariant manifold - SIM). As a result, the demanding problem of constructing SIM of any dimensions is recast into the remarkably simpler task of solving a properly devised ODE system by stiff numerical schemes available in the literature. In the same spirit, a set of equations is elaborated for local construction of the fast subspace, and possible initialization procedures for the above equations are discussed. The implementation to a detailed mechanism for combustion of hydrogen and air has been carried out, while a model with the exact Chapman-Enskog solution of the invariance equation is utilized as a benchmark. |
| title | Approximation of slow and fast dynamics in multiscale dynamical systems by the linearized Relaxation Redistribution Method |
| topic | Statistical Mechanics Dynamical Systems |
| url | https://arxiv.org/abs/1102.0730 |