Volume 26, Issue 5
An Efficient and Unconditionally Energy Stable Scheme for Simulating Solid-State Dewetting of Thin Films with Isotropic Surface Energy

Qiong-Ao Huang, Wei Jiang & Jerry Zhijian Yang

Commun. Comput. Phys., 26 (2019), pp. 1444-1470.

Published online: 2019-08

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  • Abstract

In this paper, we propose highly efficient, unconditionally energy-stable numerical schemes to approximate the isotropic phase field model of solid-state dewetting problems by using the invariant energy quadratization (IEQ) method. The phase field model is governed by the isotropic Cahn-Hilliard equation with degenerate mobilities and dynamic contact line boundary conditions. By using the backward differential formula to discretize temporal derivatives, we construct linearly first- and second-order IEQ schemes for solving the model. It can be rigorously proved that these numerical schemes are unconditionally energy-stable and satisfy the total mass conservation during the evolution. By performing numerical simulations, we demonstrate that these IEQ-based schemes (including the first-order IEQ/BDF1, second-order IEQ/BDF2) are highly efficient, accurate and energy-stable. Furthermore, many interesting dewetting phenomena (such as the hole dynamics, pinch-off), are investigated by using the proposed IEQ schemes.

  • Keywords

Solid-state dewetting, surface diffusion, phase-field model, degenerate Cahn-Hilliard equation, invariant energy quadratization, unconditionally energy-stable.

  • AMS Subject Headings

74K35, 65M06, 65M12, 35K55

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

jiangwei1007@whu.edu.cn (Qiong-Ao Huang)

zjyang.math@whu.edu.cn (Jerry Zhijian Yang)

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@Article{CiCP-26-1444, author = {Huang , Qiong-Ao and Jiang , Wei and Yang , Jerry Zhijian }, title = {An Efficient and Unconditionally Energy Stable Scheme for Simulating Solid-State Dewetting of Thin Films with Isotropic Surface Energy}, journal = {Communications in Computational Physics}, year = {2019}, volume = {26}, number = {5}, pages = {1444--1470}, abstract = {

In this paper, we propose highly efficient, unconditionally energy-stable numerical schemes to approximate the isotropic phase field model of solid-state dewetting problems by using the invariant energy quadratization (IEQ) method. The phase field model is governed by the isotropic Cahn-Hilliard equation with degenerate mobilities and dynamic contact line boundary conditions. By using the backward differential formula to discretize temporal derivatives, we construct linearly first- and second-order IEQ schemes for solving the model. It can be rigorously proved that these numerical schemes are unconditionally energy-stable and satisfy the total mass conservation during the evolution. By performing numerical simulations, we demonstrate that these IEQ-based schemes (including the first-order IEQ/BDF1, second-order IEQ/BDF2) are highly efficient, accurate and energy-stable. Furthermore, many interesting dewetting phenomena (such as the hole dynamics, pinch-off), are investigated by using the proposed IEQ schemes.

}, issn = {1991-7120}, doi = {https://doi.org/ 10.4208/cicp.2019.js60.07}, url = {http://global-sci.org/intro/article_detail/cicp/13271.html} }
TY - JOUR T1 - An Efficient and Unconditionally Energy Stable Scheme for Simulating Solid-State Dewetting of Thin Films with Isotropic Surface Energy AU - Huang , Qiong-Ao AU - Jiang , Wei AU - Yang , Jerry Zhijian JO - Communications in Computational Physics VL - 5 SP - 1444 EP - 1470 PY - 2019 DA - 2019/08 SN - 26 DO - http://dor.org/ 10.4208/cicp.2019.js60.07 UR - https://global-sci.org/intro/cicp/13271.html KW - Solid-state dewetting, surface diffusion, phase-field model, degenerate Cahn-Hilliard equation, invariant energy quadratization, unconditionally energy-stable. AB -

In this paper, we propose highly efficient, unconditionally energy-stable numerical schemes to approximate the isotropic phase field model of solid-state dewetting problems by using the invariant energy quadratization (IEQ) method. The phase field model is governed by the isotropic Cahn-Hilliard equation with degenerate mobilities and dynamic contact line boundary conditions. By using the backward differential formula to discretize temporal derivatives, we construct linearly first- and second-order IEQ schemes for solving the model. It can be rigorously proved that these numerical schemes are unconditionally energy-stable and satisfy the total mass conservation during the evolution. By performing numerical simulations, we demonstrate that these IEQ-based schemes (including the first-order IEQ/BDF1, second-order IEQ/BDF2) are highly efficient, accurate and energy-stable. Furthermore, many interesting dewetting phenomena (such as the hole dynamics, pinch-off), are investigated by using the proposed IEQ schemes.

Qiong-Ao Huang, Wei Jiang & Jerry Zhijian Yang. (2019). An Efficient and Unconditionally Energy Stable Scheme for Simulating Solid-State Dewetting of Thin Films with Isotropic Surface Energy. Communications in Computational Physics. 26 (5). 1444-1470. doi: 10.4208/cicp.2019.js60.07
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