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 |
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| Hlavní autori: | , , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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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. |
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| 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 |
| Author_xml | – sequence: 1 givenname: Yan surname: Wang fullname: Wang, Yan email: wangyanmath@yeah.net organization: Department of Mathematics, National University of Defense Technology, Changsha, 410073, China – sequence: 2 givenname: Xufeng surname: Xiao fullname: Xiao, Xufeng email: xiaoxufeng111@sina.com organization: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China – sequence: 3 givenname: Hong orcidid: 0000-0002-4417-2408 surname: Zhang fullname: Zhang, Hong email: zhanghnudt@163.com organization: Department of Mathematics, National University of Defense Technology, Changsha, 410073, China – sequence: 4 givenname: Xu surname: Qian fullname: Qian, Xu email: qianxu@nudt.edu.cn organization: Department of Mathematics, National University of Defense Technology, Changsha, 410073, China – sequence: 5 givenname: Songhe surname: Song fullname: Song, Songhe email: shsong@nudt.edu.cn organization: Department of Mathematics, National University of Defense Technology, Changsha, 410073, China |
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| Keywords | Diffusion domain method Complex domain 65M06 Multithread algorithm 82D60 Diblock copolymer melt 65Y05 Dimension splitting method |
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| 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 |
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