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A General Deterministic Treatment of Derivatives in Particle Methods

Eldredge, Jeff D. and Leonard, Anthony and Colonius, Tim (2002) A General Deterministic Treatment of Derivatives in Particle Methods. Journal of Computational Physics, 180 (2). pp. 686-709. ISSN 0021-9991. doi:10.1006/jcph.2002.7112.

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A unified approach to approximating spatial derivatives in particle methods using integral operators is presented. The approach is an extension of particle strength exchange, originally developed for treating the Laplacian in advection-diffusion problems. Kernels of high order of accuracy are constructed that can be used to approximate derivatives of any degree. A new treatment for computing derivatives near the edge of particle coverage is introduced, using "one-sided" integrals that only look for information where it is available. The use of these integral approximations in wave propagation applications is considered and their error is analyzed in this context using Fourier methods. Finally, simple tests are performed to demonstrate the characteristics of the treatment, including an assessment of the effects of particle dispersion, and their results are discussed.

Item Type:Article
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Colonius, Tim0000-0003-0326-3909
Additional Information:© 2002 Elsevier. Received 26 April 2001, revised 25 March 2002, available online 8 August 2002. The first author gratefully acknowledges support under a NSF Graduate Research Fellowship. This research was supported in part by the National Science Foundation under Grant 9501349.
Funding AgencyGrant Number
NSF Graduate Research FellowshipUNSPECIFIED
Subject Keywords:Particle methods; numerical simulation; vortex methods
Issue or Number:2
Record Number:CaltechAUTHORS:20190708-164305261
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:96934
Deposited By: Melissa Ray
Deposited On:09 Jul 2019 23:57
Last Modified:16 Nov 2021 17:24

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