An Equation Free algorithm accurately simulates macroscale shocks arising from heterogeneous microscale systems

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dc.contributor.authorMaclean, J.
dc.contributor.authorBunder, J.E.
dc.contributor.authorKevrekidis, I.G.
dc.contributor.authorRoberts, A.J.
dc.date.issued2021
dc.description.abstractScientists and engineers often create accurate, trustworthy, computational simulation schemes—but all too often these are too computationally expensive to execute over the time or spatial domain of interest. The equation-free approach is to marry such trusted simulations to a framework for numerical macroscale reduction—the patch dynamics scheme. This article extends the patch scheme to scenarios in which the trusted simulation resolves abrupt state changes on the microscale that appear as shocks on the macroscale. Accurate simulation for problems in these scenarios requires capturing the shock within a novel patch, and also modifying the patch coupling rules in the vicinity in order to maintain accuracy. With these two extensions to the patch scheme, straightforward arguments derive consistency conditions that match the usual order of accuracy for patch schemes. The new scheme is successfully tested to simulate a heterogeneous microscale partial differential equation.This technique willempower scientists and engineers to accurately and efficiently simulate, over large spatial domains, multiscale multiphysics systems that have rapid transition layers on the microscale.
dc.description.statementofresponsibilityJohn Maclean, Judith E. Bunder, Ioannis G. Kevrekidis, and Anthony J. Roberts
dc.identifier.citationIEEE Journal on Multiscale and Multiphysics Computational Techniques, 2021; 6(9335051):8-15
dc.identifier.doi10.1109/jmmct.2021.3054012
dc.identifier.issn2379-8793
dc.identifier.issn2379-8793
dc.identifier.orcidMaclean, J. [0000-0002-5533-0838]
dc.identifier.orcidBunder, J.E. [0000-0001-5355-2288]
dc.identifier.orcidRoberts, A.J. [0000-0001-8930-1552]
dc.identifier.urihttps://hdl.handle.net/2440/140009
dc.language.isoen
dc.publisherInstitute of Electrical and Electronics Engineers
dc.relation.granthttp://purl.org/au-research/grants/arc/DP150102385
dc.relation.granthttp://purl.org/au-research/grants/arc/DP180100050
dc.rights© 2021 IEEE
dc.source.urihttps://doi.org/10.1109/jmmct.2021.3054012
dc.subjectAdaptive mesh refinement; finite difference methods; numerical simulation
dc.titleAn Equation Free algorithm accurately simulates macroscale shocks arising from heterogeneous microscale systems
dc.typeJournal article
pubs.publication-statusPublished

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