Yan Wang , Xufeng Xiao , Hong Zhang , Xu Qian , Songhe Song
{"title":"Efficient diffusion domain modeling and fast numerical methods for diblock copolymer melt in complex domains","authors":"Yan Wang , Xufeng Xiao , Hong Zhang , Xu Qian , Songhe Song","doi":"10.1016/j.cpc.2024.109343","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":null,"pages":null},"PeriodicalIF":7.2000,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Physics Communications","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0010465524002662","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍:
The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper.
Computer Programs in Physics (CPiP)
These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged.
Computational Physics Papers (CP)
These are research papers in, but are not limited to, the following themes across computational physics and related disciplines.
mathematical and numerical methods and algorithms;
computational models including those associated with the design, control and analysis of experiments; and
algebraic computation.
Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.