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

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

doi:10.1007/s00466-020-01879-1

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

Journal Article · Thu Jul 30 00:00:00 EDT 2020 · Computational Mechanics

DOI:https://doi.org/10.1007/s00466-020-01879-1· OSTI ID:1666005

^[1]; Hermann, Alexander ^[1]; Seleson, Pablo ^[2]; Cyron, Christian J. ^[3]

Helmholtz-Zentrum Geesthacht (Germany). Inst. of Materials Research
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Helmholtz-Zentrum Geesthacht (Germany). Inst. of Materials Research; Hamburg Univ. of Technology (Germany). Inst. of Continuum and Materials Mechanics

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.

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Research Organization:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1666005

Journal Information:: Computational Mechanics, Vol. 66, Issue 4; ISSN 0178-7675

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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