Title: | On Solving the Poisson Equation with Discontinuities on Irregular Interfaces: GFM and VIM |
Author: |
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Date: | 2018-10-17 |
Language: | English |
Scope: | 9216703 |
University/Institute: | Háskóli Íslands University of Iceland |
School: | Verkfræði- og náttúruvísindasvið (HÍ) School of Engineering and Natural Sciences (UI) |
Department: | Iðnaðarverkfræði-, vélaverkfræði- og tölvunarfræðideild (HÍ) Faculty of Industrial Eng., Mechanical Eng. and Computer Science (UI) |
Series: | International Journal of Differential Equations;2018 |
ISSN: | 1687-9643 1687-9651 (eISSN) |
DOI: | 10.1155/2018/9216703 |
Subject: | Töluleg greining; Stærðfræðileg tölfræði |
URI: | https://hdl.handle.net/20.500.11815/1086 |
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.
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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.
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Description:Publisher's version (útgefin grein)
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Rights: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.
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