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Title: Integral approximations to classical diffusion and smoothed particle hydrodynamics

Abstract

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.

Authors:
 [1];  [2];  [3]
  1. Columbia Univ., New York, NY (United States); Pennsylvania State Univ., University Park, PA (United States)
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  3. Univ. of South Florida, Tampa, FL (United States); Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1235919
Report Number(s):
SAND-2015-0849J
Journal ID: ISSN 0045-7825; PII: S0045782514004988
Grant/Contract Number:  
AC04-94AL85000
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Computer Methods in Applied Mechanics and Engineering
Additional Journal Information:
Journal Volume: 286; Journal Issue: C; Journal ID: ISSN 0045-7825
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 97 MATHEMATICS AND COMPUTING; smooth particle hydrodynamics; classical diffusion; nonlocal diffusion; nonlocal operator; nonlocal Neumann condition; numerical approximation; integral operators; diffusion; Neumann boundary

Citation Formats

Du, Qiang, Lehoucq, R. B., and Tartakovsky, A. M. Integral approximations to classical diffusion and smoothed particle hydrodynamics. United States: N. p., 2014. Web. doi:10.1016/j.cma.2014.12.019.
Du, Qiang, Lehoucq, R. B., & Tartakovsky, A. M. Integral approximations to classical diffusion and smoothed particle hydrodynamics. United States. https://doi.org/10.1016/j.cma.2014.12.019
Du, Qiang, Lehoucq, R. B., and Tartakovsky, A. M. 2014. "Integral approximations to classical diffusion and smoothed particle hydrodynamics". United States. https://doi.org/10.1016/j.cma.2014.12.019. https://www.osti.gov/servlets/purl/1235919.
@article{osti_1235919,
title = {Integral approximations to classical diffusion and smoothed particle hydrodynamics},
author = {Du, Qiang and Lehoucq, R. B. and Tartakovsky, A. M.},
abstractNote = {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.},
doi = {10.1016/j.cma.2014.12.019},
url = {https://www.osti.gov/biblio/1235919}, journal = {Computer Methods in Applied Mechanics and Engineering},
issn = {0045-7825},
number = C,
volume = 286,
place = {United States},
year = {Wed Dec 31 00:00:00 EST 2014},
month = {Wed Dec 31 00:00:00 EST 2014}
}

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Cited by: 19 works
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Works referenced in this record:

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journal, September 1997


Conduction Modelling Using Smoothed Particle Hydrodynamics
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journal, December 2010


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Smoothed particle hydrodynamics
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Truncation error in mesh-free particle methods
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Works referencing / citing this record:

Smoothed particle hydrodynamics and its applications for multiphase flow and reactive transport in porous media
journal, March 2015


Investigating the Effects of Anisotropic Mass Transport on Dendrite Growth in High Energy Density Lithium Batteries
journal, November 2015