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On Solving the Poisson Equation with Discontinuities on Irregular Interfaces: GFM and VIM

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dc.contributor Háskóli Íslands
dc.contributor University of Iceland
dc.contributor.author Helgadottir, Asdis
dc.contributor.author Guittet, Arthur
dc.contributor.author Gibou, Frédéric
dc.date.accessioned 2019-04-01T10:38:45Z
dc.date.available 2019-04-01T10:38:45Z
dc.date.issued 2018-10-17
dc.identifier.citation Ásdís Helgadóttir, Arthur Guittet, and Frédéric Gibou, “On Solving the Poisson Equation with Discontinuities on Irregular Interfaces: GFM and VIM,” International Journal of Differential Equations, vol. 2018, Article ID 9216703, 8 pages, 2018. https://doi.org/10.1155/2018/9216703.
dc.identifier.issn 1687-9643
dc.identifier.issn 1687-9651 (eISSN)
dc.identifier.uri https://hdl.handle.net/20.500.11815/1086
dc.description Publisher's version (útgefin grein)
dc.description.abstract We analyze the accuracy of two numerical methods for the variable coefficient Poisson equation with discontinuities at an irregular interface. Solving the Poisson equation with discontinuities at an irregular interface is an essential part of solving many physical phenomena such as multiphase flows with and without phase change, in heat transfer, in electrokinetics, and in the modeling of biomolecules’ electrostatics. The first method, considered for the problem, is the widely known Ghost-Fluid Method (GFM) and the second method is the recently introduced Voronoi Interface Method (VIM). The VIM method uses Voronoi partitions near the interface to construct local configurations that enable the use of the Ghost-Fluid philosophy in one dimension. Both methods lead to symmetric positive definite linear systems. The Ghost-Fluid Method is generally first-order accurate, except in the case of both a constant discontinuity in the solution and a constant diffusion coefficient, while the Voronoi Interface Method is second-order accurate in the -norm. Therefore, the Voronoi Interface Method generally outweighs the Ghost-Fluid Method except in special case of both a constant discontinuity in the solution and a constant diffusion coefficient, where the Ghost-Fluid Method performs better than the Voronoi Interface Method. The paper includes numerical examples displaying this fact clearly and its findings can be used to determine which approach to choose based on the properties of the real life problem in hand.
dc.description.sponsorship The research of Á. Helgadóttir was supported by the University of Iceland Research Fund 2015 under HI14090070. The researches of A. Guittet and F. Gibou were supported in part by the NSF under DMS-1412695 and DMREF-1534264.
dc.format.extent 9216703
dc.language.iso en
dc.publisher Hindawi Limited
dc.relation.ispartofseries International Journal of Differential Equations;2018
dc.rights info:eu-repo/semantics/openAccess
dc.subject Töluleg greining
dc.subject Stærðfræðileg tölfræði
dc.title On Solving the Poisson Equation with Discontinuities on Irregular Interfaces: GFM and VIM
dc.type info:eu-repo/semantics/article
dcterms.license This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
dc.description.version Peer Reviewed
dc.identifier.journal International Journal of Differential Equations
dc.identifier.doi 10.1155/2018/9216703
dc.contributor.department Iðnaðarverkfræði-, vélaverkfræði- og tölvunarfræðideild (HÍ)
dc.contributor.department Faculty of Industrial Eng., Mechanical Eng. and Computer Science (UI)
dc.contributor.school Verkfræði- og náttúruvísindasvið (HÍ)
dc.contributor.school School of Engineering and Natural Sciences (UI)


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