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 and Jerry Zhijian Yang


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

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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.

  • History

Published online: 2019-08

  • AMS Subject Headings

74K35, 65M06, 65M12, 35K55

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