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dc.contributor.authorVaughan, G.L.
dc.contributor.authorHealy, Terry R.
dc.contributor.authorBryan, Karin R.
dc.contributor.authorSneyd, Alfred D.
dc.contributor.authorGorman, R.M.
dc.date.accessioned2009-01-15T22:29:48Z
dc.date.available2009-01-15T22:29:48Z
dc.date.issued2008
dc.identifier.citationVaughan, G.L., Healy, T.R., Bryan, K.R., Sneyd, A.D. & Gorman, R.M.(2008). Completeness, conservation and error in SPH for fluids. International Journal for Numerical Methods in Fluids, 56(1), 37-62.en
dc.identifier.urihttps://hdl.handle.net/10289/1790
dc.description.abstractSmoothed particle hydrodynamics (SPH) is becoming increasingly common in the numerical simulation of complex fluid flows and an understanding of the errors is necessary. Recent advances have established techniques for ensuring completeness conditions (low-order polynomials are interpolated exactly) are enforced when estimating property gradients, but the consequences on errors have not been investigated. Here, we present an expression for the error in an SPH estimate, accounting for completeness, an expression that applies to SPH generally. We revisit the derivation of the SPH equations for fluids, paying particular attention to the conservation principles. We find that a common method for enforcing completeness violates a property required of the kernel gradients, namely that gradients with respect the two position variables be equal and opposite. In such models this means conservation principles are not enforced and we present results that show this. As an aside we show the summation interpolant for density is a solution of, and may be used in the place of, the discretized, symmetrized continuity equation. Finally, we examine two examples of discretization errors, namely numerical boundary layers and the existence of crystallized states. Copyright ©2007 John Wiley & Sons, Ltd.en
dc.language.isoen
dc.publisherJohn Wiley & Sons, Ltd.en
dc.relation.urihttp://www3.interscience.wiley.com/cgi-bin/fulltext/114276224/PDFSTARTen
dc.subjectmathematicsen
dc.subjectSPHen
dc.subjectsmothes particle hydrodynamicsen
dc.subjectconservation principlesen
dc.subjectcompletenessen
dc.subjecterroren
dc.subjectfluidsen
dc.titleCompleteness, conservation and error in SPH for fluidsen
dc.typeConference Contributionen
dc.identifier.doi10.1002/fld.1530en
dc.relation.isPartOfInternational Journal for Numerical Methods in Fluidsen_NZ
pubs.begin-page37en_NZ
pubs.elements-id32516
pubs.end-page62en_NZ
pubs.issue1en_NZ
pubs.volume56en_NZ


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