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dc.contributor.authorBatty, Christopher 17:10:39 (GMT) 17:10:39 (GMT)
dc.descriptionThe final publication is available at Elsevier via © 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
dc.description.abstractThis paper introduces a two-dimensional cell-centred finite volume discretization of the Poisson problem on adaptive Cartesian quadtree grids which exhibits second order accuracy in both "the solution and its gradients, and requires no grading condition between adjacent cells. At T-junction configurations, which occur wherever resolution differs between neighboring cells, use of the standard centred difference gradient stencil requires that ghost values be constructed by interpolation. To properly recover second order accuracy in the resulting numerical gradients, prior work addressing block-structured grids and graded trees has shown that quadratic, rather than linear, interpolation is required; the gradients otherwise exhibit only first order convergence, which limits potential applications such as fluid flow. However, previous schemes fail or lose accuracy in the presence of the more complex T-junction geometries arising in the case of general non-graded quadtrees, which place no restrictions on the resolution of neighboring cells. We therefore propose novel quadratic interpolant constructions for this case that enable second order convergence by relying on stencils oriented diagonally and applied recursively as needed. The method handles complex tree topologies and large resolution jumps between neighboring cells, even along the domain boundary, and both Dirichlet and Neumann boundary conditions are supported. Numerical experiments confirm the overall second order accuracy of the method in the L-infinity norm. (C) 2016 Elsevier Inc. All rights reserved.en
dc.description.sponsorshipThis work was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada (Grant RGPIN-04360-2014).en
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International*
dc.subjectAdaptive Cartesian Gridsen
dc.subjectDifference Methodsen
dc.subjectFinite Volumeen
dc.subjectIncompressible Euler Equationsen
dc.subjectIrregular Domainsen
dc.subjectNavier-Stokes Equationsen
dc.subjectPoisson Problemen
dc.subjectProjection Methoden
dc.subjectSecond Orderen
dc.titleA cell-centred finite volume method for the Poisson problem on non-graded quadtrees with second order accurate gradientsen
dcterms.bibliographicCitationBatty, C. (2017). A cell-centred finite volume method for the Poisson problem on non-graded quadtrees with second order accurate gradients. Journal of Computational Physics, 331, 49–72.
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2David R. Cheriton School of Computer Scienceen

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