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

IF 7.2 2区 物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Computer Physics Communications Pub Date : 2024-08-08 DOI:10.1016/j.cpc.2024.109343
Yan Wang , Xufeng Xiao , Hong Zhang , Xu Qian , Songhe Song
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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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复杂域中二嵌共聚物熔体的高效扩散域建模和快速数值方法
二嵌段共聚物在复杂领域的流体力学作用下的数值模拟在学术研究和工业应用中具有重要意义。本研究的目的是为它们建立一个快速、稳定和易于实现的数值模拟框架。研究考虑了一个流体力学耦合的二嵌段共聚物相场模型,其中包括一个守恒的 Allen-Cahn-Ohta-Kawasaki 类型方程和一个不可压缩的 Navier-Stokes 方程。然而,在复杂域中对该模型进行快速数值模拟面临着巨大挑战,包括复杂边界的离散化、三维(3D)问题的巨大计算成本、多个方程之间的强非线性耦合以及保持体积守恒特性。为了克服上述困难,我们采用扩散域(DD)方法建立了一个可在规则域中计算的新修正模型,避免了复杂边界的数值离散化。然后,我们为修正模型开发了一种稳定的二阶维数分割(DS)技术。这种方法有效地将二维或三维问题分解为不同方向的一维子问题,大大提高了计算效率。在空间离散化方面,在标记和单元(MAC)网格上采用中心差分方案,并通过适当处理确保离散体积守恒。最后,通过数值实验验证了改进模型和数值方案的有效性。通过一系列数值模拟,研究了复杂域和流体动力学对二嵌段共聚物演化的影响。
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来源期刊
Computer Physics Communications
Computer Physics Communications 物理-计算机:跨学科应用
CiteScore
12.10
自引率
3.20%
发文量
287
审稿时长
5.3 months
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.
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