Decoupled, energy stable schemes for a phase-field surfactant model
KAUST DepartmentComputational Transport Phenomena Lab
Earth Science and Engineering Program
Physical Science and Engineering (PSE) Division
KAUST Grant NumberBAS/1/1351-01-01
Online Publication Date2018-07-18
Print Publication Date2018-12
Permanent link to this recordhttp://hdl.handle.net/10754/628802
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AbstractIn this paper, we construct several linear, decoupled and energy stable schemes for a phase-field surfactant model, in which the free energy functional contains a fourth-order Ginzburg–Landau double well potential, a logarithmic Flory–Huggins potential and two nonlinear coupling terms. Several scalar auxiliary variables (SAV) are introduced to transform the governing system into an equivalent form, allowing the nonlinear potentials to be treated efficiently and semi-explicitly. At each time step, the schemes involve solving only two linear elliptic differential equations, and computations of two phase-field variables are totally decoupled. Moreover, the local concentration of surfactants can be obtained in an “explicit” way. We further establish a rigorous proof of unconditional energy stability for the semi-implicit schemes. Numerical results in both two and three dimensions are obtained, which demonstrate that the proposed schemes are accurate, efficient, easy-to-implement and unconditionally energy stable.
CitationZhu G, Kou J, Sun S, Yao J, Li A (2018) Decoupled, energy stable schemes for a phase-field surfactant model. Computer Physics Communications 233: 67–77. Available: http://dx.doi.org/10.1016/j.cpc.2018.07.003.
SponsorsJun Yao and Guangpu Zhu acknowledge that this work was supported by the National Science and Technology Major Project (2016ZX05011-001), the NSF of China (51490654, 51504276, and 51304232), and the Innovative Project of China University of Petroleum (YCX2017021). The work of Shuyu Sun and Jisheng Kou was supported by the KAUST research fund awarded to the Computational Transport Phenomena Laboratory at KAUST through the Grant BAS/1/1351-01-01.
JournalComputer Physics Communications