Efficient diffusion domain modeling and fast numerical methods for diblock copolymer melt in complex domains

The numerical simulation of diblock copolymers under hydrodynamic action in complex domains is of great significance in academic research and industrial applications. The purpose of this study is to establish a fast, stable, and easily implementable numerical simulation framework for them. A hydrody...

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Vydané v:Computer physics communications Ročník 305; s. 109343
Hlavní autori: Wang, Yan, Xiao, Xufeng, Zhang, Hong, Qian, Xu, Song, Songhe
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 01.12.2024
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ISSN:0010-4655
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Abstract The numerical simulation of diblock copolymers under hydrodynamic action in complex domains is of great significance in academic research and industrial applications. The purpose of this study is to establish a fast, stable, and easily implementable numerical simulation framework for them. A hydrodynamically coupled diblock copolymer phase field model is considered, which includes a conserved Allen-Cahn-Ohta-Kawasaki type equation and an incompressible Navier-Stokes equation. However, rapid numerical simulation of the model in complex domains faces significant challenges, including discretization of complex boundaries, huge computational costs of three-dimensional (3D) problems, strong nonlinear coupling between multiple equations, and preserving the volume conservation properties. To overcome the above difficulties, a new modified model that can be computed in the regular domain is established by diffusion domain (DD) method, avoiding numerical discretization of complex boundaries. Then, we develop a stabilized second-order dimension splitting (DS) technique for the modified model. This approach effectively decomposes 2D or 3D problems into 1D sub-problems in different directions, significantly improving the computation efficiency. For spatial discretization, the central difference scheme is applied on mark and cell (MAC) grid, and the discrete volume conservation is ensured by proper processing. Finally, the efficacy of the modified model and numerical scheme is verified through numerical experiments. A series of numerical simulations are performed to investigate the effects of complex domains and fluid dynamics on the evolution of diblock copolymers.
AbstractList The numerical simulation of diblock copolymers under hydrodynamic action in complex domains is of great significance in academic research and industrial applications. The purpose of this study is to establish a fast, stable, and easily implementable numerical simulation framework for them. A hydrodynamically coupled diblock copolymer phase field model is considered, which includes a conserved Allen-Cahn-Ohta-Kawasaki type equation and an incompressible Navier-Stokes equation. However, rapid numerical simulation of the model in complex domains faces significant challenges, including discretization of complex boundaries, huge computational costs of three-dimensional (3D) problems, strong nonlinear coupling between multiple equations, and preserving the volume conservation properties. To overcome the above difficulties, a new modified model that can be computed in the regular domain is established by diffusion domain (DD) method, avoiding numerical discretization of complex boundaries. Then, we develop a stabilized second-order dimension splitting (DS) technique for the modified model. This approach effectively decomposes 2D or 3D problems into 1D sub-problems in different directions, significantly improving the computation efficiency. For spatial discretization, the central difference scheme is applied on mark and cell (MAC) grid, and the discrete volume conservation is ensured by proper processing. Finally, the efficacy of the modified model and numerical scheme is verified through numerical experiments. A series of numerical simulations are performed to investigate the effects of complex domains and fluid dynamics on the evolution of diblock copolymers.
ArticleNumber 109343
Author Qian, Xu
Zhang, Hong
Xiao, Xufeng
Song, Songhe
Wang, Yan
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Keywords Diffusion domain method
Complex domain
65M06
Multithread algorithm
82D60
Diblock copolymer melt
65Y05
Dimension splitting method
Language English
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Snippet The numerical simulation of diblock copolymers under hydrodynamic action in complex domains is of great significance in academic research and industrial...
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StartPage 109343
SubjectTerms Complex domain
Diblock copolymer melt
Diffusion domain method
Dimension splitting method
Multithread algorithm
Title Efficient diffusion domain modeling and fast numerical methods for diblock copolymer melt in complex domains
URI https://dx.doi.org/10.1016/j.cpc.2024.109343
Volume 305
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