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Truncation error in mesh-free particle methods

ARAN - Access to Research at NUI Galway

Show simple item record Quinlan, Nathan J. en Basa, Mihai en Lastiwka, Martin en 2010-07-06T16:11:19Z en 2010-07-06T16:11:19Z en 2006-06-25 en
dc.identifier.citation Quinlan, N. J., Basa, M., & Lastiwka, M. (2006). Truncation error in mesh-free particle methods. International Journal for Numerical Methods in Engineering, 66(13), 2064-2085. en
dc.identifier.uri en
dc.description.abstract A truncation error analysis has been developed for the approximation of spatial derivatives in smoothed particle hydrodynamics (SPH) and related first-order consistent methods such as the first-order form of the reproducing kernel particle method. Error is shown to depend on both the smoothing length h and the ratio of particle spacing to smoothing length, x/h. For uniformly spaced particles in one dimension, analysis shows that as h is reduced while maintaining constant x/h, error decays as h2 until a limiting discretization error is reached, which is independent of h. If x/h is reduced while maintaining constant h (i.e. if the number of neighbours per particle is increased), error decreases at a rate which depends on the kernel function's smoothness. When particles are distributed non-uniformly, error can grow as h is reduced with constant x/h. First-order consistent methods are shown to remove this divergent behaviour. Numerical experiments confirm the theoretical analysis for one dimension, and indicate that the main results are also true in three dimensions. This investigation highlights the complexity of error behaviour in SPH, and shows that the roles of both h and x/h must be considered when choosing particle distributions and smoothing lengths. en
dc.description.sponsorship IRCSET en
dc.format application/pdf en
dc.language.iso en en
dc.subject Error analysis en
dc.subject Particle methods en
dc.subject Meshless methods en
dc.subject Meshfree methods en
dc.subject Smoothed particle hydrodynamics en
dc.title Truncation error in mesh-free particle methods en
dc.type Article en
dc.local.publishedsource en
dc.description.peer-reviewed peer-reviewed en

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