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COUPLE MICROSCALE PERIODIC PATCHES TO SIMULATE MACROSCALE EMERGENT DYNAMICS

Part of: Approximation methods and numerical treatment of dynamical systems Mathematical economics Basic methods in fluid mechanics Numerical problems in dynamical systems

Published online by Cambridge University Press:  30 January 2018

HAMMAD ALOTAIBI Open the ORCID record for HAMMAD ALOTAIBI [Opens in a new window] ,
BARRY COX Open the ORCID record for BARRY COX [Opens in a new window]  and
A. J. ROBERTS Open the ORCID record for A. J. ROBERTS [Opens in a new window]
HAMMAD ALOTAIBI
Affiliation:
School of Mathematical Sciences, University of Adelaide, South Australia, Australia email hammad.alotaibi@adelaide.edu.au, barry.cox@adelaide.edu.au, anthony.roberts@adelaide.edu.au
BARRY COX
Affiliation:
School of Mathematical Sciences, University of Adelaide, South Australia, Australia email hammad.alotaibi@adelaide.edu.au, barry.cox@adelaide.edu.au, anthony.roberts@adelaide.edu.au
A. J. ROBERTS*
Affiliation:
School of Mathematical Sciences, University of Adelaide, South Australia, Australia email hammad.alotaibi@adelaide.edu.au, barry.cox@adelaide.edu.au, anthony.roberts@adelaide.edu.au
*
✉anthony.roberts@adelaide.edu.au
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Abstract

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Macroscale “continuum” level predictions are made by a new way to construct computationally efficient “wrappers” around fine-scale, microscopic, detailed descriptions of dynamical systems, such as molecular dynamics. It is often significantly easier to code a microscale simulator with periodicity: so the challenge addressed here is to develop a scheme that uses only a given periodic microscale simulator; specifically, one for atomistic dynamics. Numerical simulations show that applying a suitable proportional controller within “action regions” of a patch of atomistic simulation effectively predicts the macroscale transport of heat. Theoretical analysis establishes that such an approach will generally be effective and efficient, and also determines good values for the strength of the proportional controller. This work has the potential to empower systematic analysis and understanding at a macroscopic system level when only a given microscale simulator is available.

Keywords

macroscale dynamicsemergenceperiodic microscalepatch schemeequation-free analysis

MSC classification

Primary: 37M05: Simulation
Secondary: 65P20: Numerical chaos 76M28: Particle methods and lattice-gas methods 91B69: Heterogeneous agent models
Type
Research Article
Information
The ANZIAM Journal , Volume 59 , Issue 3 , January 2018 , pp. 313 - 334
Copyright
© 2018 Australian Mathematical Society 

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