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Discretization correction of general integral PSE Operators for particle methods


Schrader, Birte; Reboux, Sylvain; Sbalzarini, Ivo F (2010). Discretization correction of general integral PSE Operators for particle methods. Journal of Computational Physics, 229(11):4159-4182.

Abstract

The general integral particle strength exchange (PSE) operators [J.D. Eldredge, A. Leonard, and T. Colonius, J. Comput. Phys. 180, 686–709 (2002)] approximate derivatives on scattered particle locations to any desired order of accuracy. Convergence is, however, limited to a certain range of resolutions. For high-resolution discretizations, the constant discretization error dominates and prevents further convergence. We discuss a consistent discretization correction framework for PSE operators that yields the desired rate of convergence for any resolution, both on uniform Cartesian and irregular particle distributions, as well as near boundaries. These discretization-corrected (DC) PSE operators also have no overlap condition, enabling the kernel width to become arbitrarily small for constant interparticle spacing. We show that, on uniform Cartesian particle distributions, this leads to a seamless transition between DC PSE operators and classical finite difference stencils. We further identify relationships between DC PSE operators and operators used in corrected smoothed particle hydrodynamics and reproducing kernel particle methods. We analyze the presented DC PSE operators with respect to accuracy, rate of convergence, computational efficiency, numerical dispersion, numerical diffusion, and stability.

Abstract

The general integral particle strength exchange (PSE) operators [J.D. Eldredge, A. Leonard, and T. Colonius, J. Comput. Phys. 180, 686–709 (2002)] approximate derivatives on scattered particle locations to any desired order of accuracy. Convergence is, however, limited to a certain range of resolutions. For high-resolution discretizations, the constant discretization error dominates and prevents further convergence. We discuss a consistent discretization correction framework for PSE operators that yields the desired rate of convergence for any resolution, both on uniform Cartesian and irregular particle distributions, as well as near boundaries. These discretization-corrected (DC) PSE operators also have no overlap condition, enabling the kernel width to become arbitrarily small for constant interparticle spacing. We show that, on uniform Cartesian particle distributions, this leads to a seamless transition between DC PSE operators and classical finite difference stencils. We further identify relationships between DC PSE operators and operators used in corrected smoothed particle hydrodynamics and reproducing kernel particle methods. We analyze the presented DC PSE operators with respect to accuracy, rate of convergence, computational efficiency, numerical dispersion, numerical diffusion, and stability.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:Special Collections > SystemsX.ch
Special Collections > SystemsX.ch > Research, Technology and Development Projects > LipidX
Special Collections > SystemsX.ch > Research, Technology and Development Projects > WingX
Dewey Decimal Classification:570 Life sciences; biology
Language:English
Date:2010
Deposited On:05 Jul 2013 11:28
Last Modified:07 Dec 2017 21:38
Publisher:Elsevier
ISSN:0021-9991
Publisher DOI:https://doi.org/10.1016/j.jcp.2010.02.004

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