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

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.

Subjects

Absorbing boundary conditions

Corrosion

Nonlocal diffusion

Peridynamic diffusion model

Unbounded domain

DDC Class

600: Technik

More Funding Information

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 I2B-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.

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