Efficient and accurate numerical schemes for a hydro-dynamically coupled phase field diblock copolymer model

JOURNAL OF COMPUTATIONAL PHYSICS

卷:341

Article

Cheng, Qing^1,2  Yang, Xiaofeng³  Shen, Jie⁴ 

[1] Xiamen Univ, Fujian Prov Key Lab Math Modeling & High Performa, Xiamen 361005, Fujian, Peoples R China

[2] Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China

[3] Univ South Carolina, Dept Math, Columbia, SC 29208 USA

[4] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

关键词: Phase-field;    Diblock copolymer;    Navier-Stokes;    Invariant energy quadratization;    Energy stability;   

DOI  :  10.1016/j.jcp.2017.04.010

来源: Elsevier

【 摘 要 】

In this paper, we consider numerical approximations of a hydro-dynamically coupled phase field diblock copolymer model, in which the free energy contains a kinetic potential, a gradient entropy, a Ginzburg-Landau double well potential, and a long range nonlocal type potential. We develop a set of second order time marching schemes for this system using the Invariant Energy Quadratization approach for the double well potential, the projection method for the Navier-Stokes equation, and a subtle implicit-explicit treatment for the stress and convective term. The resulting schemes are linear and lead to symmetric positive definite systems at each time step, thus they can be efficiently solved. We further prove that these schemes are unconditionally energy stable. Various numerical experiments are performed to validate the accuracy and energy stability of the proposed schemes. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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