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:
-
- 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)
- 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:
- 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. Wed .
"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},
journal = {Computer Methods in Applied Mechanics and Engineering},
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}
}
Web of Science
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