A computational strategy for multiscale systems with applications to Lorenz 96 model

Ibrahim Fatkullin; Eric Vanden-Eijnden

doi:10.1016/j.jcp.2004.04.013

A computational strategy for multiscale systems with applications to Lorenz 96 model

Ibrahim Fatkullin, Eric Vanden-Eijnden

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Numerical schemes for systems with multiple spatio-temporal scales are investigated. The multiscale schemes use asymptotic results for this type of systems which guarantee the existence of an effective dynamics for some suitably defined modes varying slowly on the largest scales. The multiscale schemes are analyzed in general, then illustrated on a specific example of a moderately large deterministic system displaying chaotic behavior due to Lorenz. Issues like consistency, accuracy, and efficiency are discussed in detail. The role of possible hidden slow variables as well as additional effects arising on the diffusive time-scale are also investigated. As a byproduct we obtain a rather complete characterization of the effective dynamics in Lorenz model.

Original language	English (US)
Pages (from-to)	605-638
Number of pages	34
Journal	Journal of Computational Physics
Volume	200
Issue number	2
DOIs	https://doi.org/10.1016/j.jcp.2004.04.013
State	Published - Nov 1 2004

Keywords

Averaging techniques
Effective dynamics
Heterogeneous Multiscale Method (HMM)
Lorenz 96 model
Mode reduction
Multiscale numerical methods

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/j.jcp.2004.04.013

Cite this

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title = "A computational strategy for multiscale systems with applications to Lorenz 96 model",

abstract = "Numerical schemes for systems with multiple spatio-temporal scales are investigated. The multiscale schemes use asymptotic results for this type of systems which guarantee the existence of an effective dynamics for some suitably defined modes varying slowly on the largest scales. The multiscale schemes are analyzed in general, then illustrated on a specific example of a moderately large deterministic system displaying chaotic behavior due to Lorenz. Issues like consistency, accuracy, and efficiency are discussed in detail. The role of possible hidden slow variables as well as additional effects arising on the diffusive time-scale are also investigated. As a byproduct we obtain a rather complete characterization of the effective dynamics in Lorenz model.",

keywords = "Averaging techniques, Effective dynamics, Heterogeneous Multiscale Method (HMM), Lorenz 96 model, Mode reduction, Multiscale numerical methods",

author = "Ibrahim Fatkullin and Eric Vanden-Eijnden",

note = "Funding Information: We thank D. Cai, A.J. Chorin, W. E, D. Liu and A.J. Majda for interesting discussions. E.V.-E. is partially supported by NSF via grants DMS01-01439, DMS02-09959 and DMS02-39625. ",

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AU - Fatkullin, Ibrahim

AU - Vanden-Eijnden, Eric

N1 - Funding Information: We thank D. Cai, A.J. Chorin, W. E, D. Liu and A.J. Majda for interesting discussions. E.V.-E. is partially supported by NSF via grants DMS01-01439, DMS02-09959 and DMS02-39625.

PY - 2004/11/1

Y1 - 2004/11/1

N2 - Numerical schemes for systems with multiple spatio-temporal scales are investigated. The multiscale schemes use asymptotic results for this type of systems which guarantee the existence of an effective dynamics for some suitably defined modes varying slowly on the largest scales. The multiscale schemes are analyzed in general, then illustrated on a specific example of a moderately large deterministic system displaying chaotic behavior due to Lorenz. Issues like consistency, accuracy, and efficiency are discussed in detail. The role of possible hidden slow variables as well as additional effects arising on the diffusive time-scale are also investigated. As a byproduct we obtain a rather complete characterization of the effective dynamics in Lorenz model.

AB - Numerical schemes for systems with multiple spatio-temporal scales are investigated. The multiscale schemes use asymptotic results for this type of systems which guarantee the existence of an effective dynamics for some suitably defined modes varying slowly on the largest scales. The multiscale schemes are analyzed in general, then illustrated on a specific example of a moderately large deterministic system displaying chaotic behavior due to Lorenz. Issues like consistency, accuracy, and efficiency are discussed in detail. The role of possible hidden slow variables as well as additional effects arising on the diffusive time-scale are also investigated. As a byproduct we obtain a rather complete characterization of the effective dynamics in Lorenz model.

KW - Averaging techniques

KW - Effective dynamics

KW - Heterogeneous Multiscale Method (HMM)

KW - Lorenz 96 model

KW - Mode reduction

KW - Multiscale numerical methods

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A computational strategy for multiscale systems with applications to Lorenz 96 model

Abstract

Keywords

ASJC Scopus subject areas

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