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Title: Integral approximations to classical diffusion and smoothed particle hydrodynamics

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:
OSTI Identifier:
1235919
Report Number(s):
SAND--2015-0849J
Journal ID: ISSN 0045-7825; PII: S0045782514004988
Grant/Contract Number:
AC04-94AL85000
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
Research Org:
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
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