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Title: Dirichlet absorbing boundary conditions for classical and peridynamic diffusion-type models

Abstract

Diffusion-type problems in (nearly) unbounded domains play important roles in various fields of fluid dynamics, biology, and materials science. The aim of this paper is to construct accurate absorbing boundary conditions (ABCs) suitable for classical (local) as well as nonlocal peridynamic (PD) diffusion models. The main focus of the present study is on the PD diffusion formulation. The majority of the PD diffusion models proposed so far are applied to bounded domains only. In this study, we propose an effective way to handle unbounded domains both with PD and classical diffusion models. For the former, we employ a meshfree discretization, whereas for the latter the finite element method (FEM) is employed. The proposed ABCs are time-dependent and Dirichlet-type, making the approach easy to implement in the available models. The performance of the approach, in terms of accuracy and stability, is illustrated by numerical examples in 1D, 2D, and 3D.

Authors:
ORCiD logo [1];  [1];  [2];  [3]
  1. Helmholtz-Zentrum Geesthacht (Germany). Inst. of Materials Research
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
  3. Helmholtz-Zentrum Geesthacht (Germany). Inst. of Materials Research; Hamburg Univ. of Technology (Germany). Inst. of Continuum and Materials Mechanics
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1666005
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
Computational Mechanics
Additional Journal Information:
Journal Volume: 66; Journal Issue: 4; Journal ID: ISSN 0178-7675
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
Peridynamic diffusion model; absorbing boundary conditions; nonlocal diffusion; corrosion; unbounded domain

Citation Formats

Shojaei, Arman, Hermann, Alexander, Seleson, Pablo, and Cyron, Christian J. Dirichlet absorbing boundary conditions for classical and peridynamic diffusion-type models. United States: N. p., 2020. Web. doi:10.1007/s00466-020-01879-1.
Shojaei, Arman, Hermann, Alexander, Seleson, Pablo, & Cyron, Christian J. Dirichlet absorbing boundary conditions for classical and peridynamic diffusion-type models. United States. doi:10.1007/s00466-020-01879-1.
Shojaei, Arman, Hermann, Alexander, Seleson, Pablo, and Cyron, Christian J. Thu . "Dirichlet absorbing boundary conditions for classical and peridynamic diffusion-type models". United States. doi:10.1007/s00466-020-01879-1. https://www.osti.gov/servlets/purl/1666005.
@article{osti_1666005,
title = {Dirichlet absorbing boundary conditions for classical and peridynamic diffusion-type models},
author = {Shojaei, Arman and Hermann, Alexander and Seleson, Pablo and Cyron, Christian J.},
abstractNote = {Diffusion-type problems in (nearly) unbounded domains play important roles in various fields of fluid dynamics, biology, and materials science. The aim of this paper is to construct accurate absorbing boundary conditions (ABCs) suitable for classical (local) as well as nonlocal peridynamic (PD) diffusion models. The main focus of the present study is on the PD diffusion formulation. The majority of the PD diffusion models proposed so far are applied to bounded domains only. In this study, we propose an effective way to handle unbounded domains both with PD and classical diffusion models. For the former, we employ a meshfree discretization, whereas for the latter the finite element method (FEM) is employed. The proposed ABCs are time-dependent and Dirichlet-type, making the approach easy to implement in the available models. The performance of the approach, in terms of accuracy and stability, is illustrated by numerical examples in 1D, 2D, and 3D.},
doi = {10.1007/s00466-020-01879-1},
journal = {Computational Mechanics},
number = 4,
volume = 66,
place = {United States},
year = {2020},
month = {7}
}

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