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A self-organizing Lagrangian particle method for adaptive-resolution advection–diffusion simulations


Reboux, Sylvain; Schrader, Birte; Sbalzarini, Ivo F (2012). A self-organizing Lagrangian particle method for adaptive-resolution advection–diffusion simulations. Journal of Computational Physics, 231(9):3623-3646.

Abstract

We present a novel adaptive-resolution particle method for continuous parabolic problems. In this method, particles self-organize in order to adapt to local resolution requirements. This is achieved by pseudo forces that are designed so as to guarantee that the solution is always well sampled and that no holes or clusters develop in the particle distribution. The particle sizes are locally adapted to the length scale of the solution. Differential operators are consistently evaluated on the evolving set of irregularly distributed particles of varying sizes using discretization-corrected operators. The method does not rely on any global transforms or mapping functions. After presenting the method and its error analysis, we demonstrate its capabilities and limitations on a set of two- and three-dimensional benchmark problems. These include advection-diffusion, the Burgers equation, the Buckley-Leverett five-spot problem, and curvature-driven level-set surface refinement.

Abstract

We present a novel adaptive-resolution particle method for continuous parabolic problems. In this method, particles self-organize in order to adapt to local resolution requirements. This is achieved by pseudo forces that are designed so as to guarantee that the solution is always well sampled and that no holes or clusters develop in the particle distribution. The particle sizes are locally adapted to the length scale of the solution. Differential operators are consistently evaluated on the evolving set of irregularly distributed particles of varying sizes using discretization-corrected operators. The method does not rely on any global transforms or mapping functions. After presenting the method and its error analysis, we demonstrate its capabilities and limitations on a set of two- and three-dimensional benchmark problems. These include advection-diffusion, the Burgers equation, the Buckley-Leverett five-spot problem, and curvature-driven level-set surface refinement.

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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
Dewey Decimal Classification:570 Life sciences; biology
Language:English
Date:2012
Deposited On:05 Jul 2013 12:09
Last Modified:05 Apr 2016 16:51
Publisher:Elsevier
ISSN:0021-9991
Publisher DOI:https://doi.org/10.1016/j.jcp.2012.01.026

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