Integral approximations to classical diffusion and smoothed particle hydrodynamics

Du, Qiang; Lehoucq, R. B.; Tartakovsky, A. M.

doi:10.1016/j.cma.2014.12.019

Title: Integral approximations to classical diffusion and smoothed particle hydrodynamics

Journal Article · Wed Dec 31 00:00:00 EST 2014 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2014.12.019· OSTI ID:1235919

Du, Qiang ^[1]; Lehoucq, R. B. ^[2]; Tartakovsky, A. M. ^[3]

Columbia Univ., New York, NY (United States); Pennsylvania State Univ., University Park, PA (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Univ. of South Florida, Tampa, FL (United States); Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

The contribution of the paper is the approximation of a classical diffusion operator by an integral equation with a volume constraint. A particular focus is on classical diffusion problems associated with Neumann boundary conditions. By exploiting this approximation, we can also approximate other quantities such as the flux out of a domain. Our analysis of the model equation on the continuum level is closely related to the recent work on nonlocal diffusion and peridynamic mechanics. In particular, we elucidate the role of a volumetric constraint as an approximation to a classical Neumann boundary condition in the presence of physical boundary. The volume-constrained integral equation then provides the basis for accurate and robust discretization methods. As a result, an immediate application is to the understanding and improvement of the Smoothed Particle Hydrodynamics (SPH) method.

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Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1235919

Report Number(s):: SAND-2015-0849J; PII: S0045782514004988

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Vol. 286, Issue C; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 19 works

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References (26)

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Smoothed particle hydrodynamics and its applications for multiphase flow and reactive transport in porous media Tartakovsky, A. M.; Trask, N.; Pan, K. Computational Geosciences, Vol. 20, Issue 4 https://doi.org/10.1007/s10596-015-9468-9	journal	March 2015
Investigating the Effects of Anisotropic Mass Transport on Dendrite Growth in High Energy Density Lithium Batteries Tan, Jinwang; Tartakovsky, Alexandre M.; Ferris, Kim Journal of The Electrochemical Society, Vol. 163, Issue 2 https://doi.org/10.1149/2.0951602jes	journal	November 2015

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