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Title: A space-time adaptive finite element method with exponential time integrator for the phase field model of pitting corrosion

Abstract

In this paper we propose a space-time adaptive finite element method for the phase field model of pitting corrosion, which is a parabolic partial differential equation system consisting of a phase variable and a concentration variable. A major challenge in solving this phase field model is that the problem is very stiff, which makes the time step size extremely small for standard temporal discretizations. Another difficulty is that a high spatial resolution is required to capture the steep gradients within the diffused interface, which results in very large number of degrees of freedom for uniform meshes. To overcome the stiffness of this model, we combine the Rosenbrock–Euler exponential integrator with Crank–Nicolson scheme for the temporal discretization. Moreover, by exploiting the fact that the speed of the corroding interface decreases with time, we derive an adaptive time stepping formula. For the spatial approximation, we propose a simple and efficient strategy to generate adaptive meshes that reduces the computational cost significantly. Thus, the proposed method utilizes local adaptivity and mesh refinement for efficient simulation of the corrosive dissolution over long times in heterogeneous media with complex microstructures. We also present an extensive set of numerical experiments in both two and three dimensionalmore » spaces to demonstrate efficiency and robustness of the proposed method.« less

Authors:
 [1];  [2];  [3]; ORCiD logo [4]
+ Show Author Affiliations
  1. Huazhong Univ. of Science and Technology, Wuhan (China)
  2. Univ. of South Carolina, Columbia, SC (United States)
  3. Univ. of South Carolina, Columbia, SC (United States); The Hong Kong Polytechnic Univ. (Hong Kong)
  4. Vanderbilt Univ., Nashville, TN (United States)
Publication Date:
Research Org.:
Univ. of South Carolina, Columbia, SC (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
OSTI Identifier:
1803035
Alternate Identifier(s):
OSTI ID: 1593202
Grant/Contract Number:  
SC0016540; SC0020270
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 406; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; pitting corrosion; phase field model; finite element method; adaptivity; exponential integrator; semi-implicit scheme

Citation Formats

Gao, Huadong, Ju, Lili, Li, Xiao, and Duddu, Ravindra. A space-time adaptive finite element method with exponential time integrator for the phase field model of pitting corrosion. United States: N. p., 2019. Web. doi:10.1016/j.jcp.2019.109191.
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Gao, Huadong, Ju, Lili, Li, Xiao, & Duddu, Ravindra. A space-time adaptive finite element method with exponential time integrator for the phase field model of pitting corrosion. United States. https://doi.org/10.1016/j.jcp.2019.109191
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Gao, Huadong, Ju, Lili, Li, Xiao, and Duddu, Ravindra. Fri . "A space-time adaptive finite element method with exponential time integrator for the phase field model of pitting corrosion". United States. https://doi.org/10.1016/j.jcp.2019.109191. https://www.osti.gov/servlets/purl/1803035.
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@article{osti_1803035,
title = {A space-time adaptive finite element method with exponential time integrator for the phase field model of pitting corrosion},
author = {Gao, Huadong and Ju, Lili and Li, Xiao and Duddu, Ravindra},
abstractNote = {In this paper we propose a space-time adaptive finite element method for the phase field model of pitting corrosion, which is a parabolic partial differential equation system consisting of a phase variable and a concentration variable. A major challenge in solving this phase field model is that the problem is very stiff, which makes the time step size extremely small for standard temporal discretizations. Another difficulty is that a high spatial resolution is required to capture the steep gradients within the diffused interface, which results in very large number of degrees of freedom for uniform meshes. To overcome the stiffness of this model, we combine the Rosenbrock–Euler exponential integrator with Crank–Nicolson scheme for the temporal discretization. Moreover, by exploiting the fact that the speed of the corroding interface decreases with time, we derive an adaptive time stepping formula. For the spatial approximation, we propose a simple and efficient strategy to generate adaptive meshes that reduces the computational cost significantly. Thus, the proposed method utilizes local adaptivity and mesh refinement for efficient simulation of the corrosive dissolution over long times in heterogeneous media with complex microstructures. We also present an extensive set of numerical experiments in both two and three dimensional spaces to demonstrate efficiency and robustness of the proposed method.},
doi = {10.1016/j.jcp.2019.109191},
journal = {Journal of Computational Physics},
number = ,
volume = 406,
place = {United States},
year = {Fri Dec 20 00:00:00 EST 2019},
month = {Fri Dec 20 00:00:00 EST 2019}
}
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https://doi.org/10.1016/j.jcp.2019.109191
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