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

Arman Shojaei; Alexander Hermann; Pablo Seleson; Christian J. Cyron

doi:10.1007/s00466-020-01879-1

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

Arman Shojaei, Alexander Hermann, Pablo Seleson, Christian J. Cyron

Multiscale Methods

Research output: Contribution to journal › Article › peer-review

52 Scopus citations

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.

Original language	English
Pages (from-to)	773-793
Number of pages	21
Journal	Computational Mechanics
Volume	66
Issue number	4
DOIs	https://doi.org/10.1007/s00466-020-01879-1
State	Published - Oct 1 2020

Funding

Open Access funding provided by Projekt DEAL. This work was funded by the VirMat project of the Helmholtz Association of German Research Centres and the B-project “Virtual Materials Design for Degradable Magnesium Implants” of HZG. Research sponsored by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U.S. Department of Energy. This manuscript has been co-authored by UT-Battelle, LLC, under Contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan ( http://energy.gov/downloads/doe-public-access-plan ).

Keywords

Absorbing boundary conditions
Corrosion
Nonlocal diffusion
Peridynamic diffusion model
Unbounded domain

Access to Document

10.1007/s00466-020-01879-1

Cite this

@article{f3a622f597184946ae38301511bc6493,

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.",

keywords = "Absorbing boundary conditions, Corrosion, Nonlocal diffusion, Peridynamic diffusion model, Unbounded domain",

author = "Arman Shojaei and Alexander Hermann and Pablo Seleson and Cyron, \{Christian J.\}",

note = "Publisher Copyright: {\textcopyright} 2020, The Author(s).",

year = "2020",

month = oct,

day = "1",

doi = "10.1007/s00466-020-01879-1",

language = "English",

volume = "66",

pages = "773--793",

journal = "Computational Mechanics",

issn = "0178-7675",

publisher = "Springer",

number = "4",

}

TY - JOUR

T1 - Dirichlet absorbing boundary conditions for classical and peridynamic diffusion-type models

AU - Shojaei, Arman

AU - Hermann, Alexander

AU - Seleson, Pablo

AU - Cyron, Christian J.

PY - 2020/10/1

Y1 - 2020/10/1

N2 - 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.

AB - 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.

KW - Absorbing boundary conditions

KW - Corrosion

KW - Nonlocal diffusion

KW - Peridynamic diffusion model

KW - Unbounded domain

UR - https://www.scopus.com/pages/publications/85088833260

U2 - 10.1007/s00466-020-01879-1

DO - 10.1007/s00466-020-01879-1

M3 - Article

AN - SCOPUS:85088833260

SN - 0178-7675

VL - 66

SP - 773

EP - 793

JO - Computational Mechanics

JF - Computational Mechanics

IS - 4

ER -

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

Abstract

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this