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dc.contributor.authorZhu, Guangpu
dc.contributor.authorChen, Huangxin
dc.contributor.authorLi, Aifen
dc.contributor.authorSun, Shuyu
dc.contributor.authorYao, Jun
dc.date.accessioned2018-02-07T07:02:23Z
dc.date.available2018-02-07T07:02:23Z
dc.date.issued2020-03-04
dc.date.submitted2019-02-20
dc.identifier.citationZhu, G., Chen, H., Li, A., Sun, S., & Yao, J. (2020). Fully discrete energy stable scheme for a phase-field moving contact line model with variable densities and viscosities. Applied Mathematical Modelling, 83, 614–639. doi:10.1016/j.apm.2020.02.022
dc.identifier.issn0307-904X
dc.identifier.doi10.1016/j.apm.2020.02.022
dc.identifier.urihttp://hdl.handle.net/10754/627045
dc.description.abstractIn this study, we propose a fully discrete energy stable scheme for the phase-field moving contact line model with variable densities and viscosities. The mathematical model comprises a Cahn–Hilliard equation, Navier–Stokes equation, and the generalized Navier boundary condition for the moving contact line. A scalar auxiliary variable is employed to transform the governing system into an equivalent form, thereby allowing the double well potential to be treated semi-explicitly. A stabilization term is added to balance the explicit nonlinear term originating from the surface energy at the fluid–solid interface. A pressure stabilization method is used to decouple the velocity and pressure computations. Some subtle implicit–explicit treatments are employed to deal with convention and stress terms. We establish a rigorous proof of the energy stability for the proposed time-marching scheme. A finite difference method based on staggered grids is then used to spatially discretize the constructed time-marching scheme. We also prove that the fully discrete scheme satisfies the discrete energy dissipation law. Our numerical results demonstrate the accuracy and energy stability of the proposed scheme. Using our numerical scheme, we analyze the contact line dynamics based on a shear flow-driven droplet sliding case. Three-dimensional droplet spreading is also investigated based on a chemically patterned surface. Our numerical simulation accurately predicts the expected energy evolution and it successfully reproduces the expected phenomena where an oil droplet contracts inward on a hydrophobic zone and then spreads outward rapidly on a hydrophilic zone.
dc.description.sponsorshipGuangpu Zhu and Huangxin Chen contributed equally to this study. Jun Yao and Guangpu Zhu acknowledge that this study was supported by the National Science and Technology Major Project (2016ZX05011-001) and the NSF of China (51804325 and 51674280). Huangxin Chen was supported by the NSF of China (Grant Nos. 11771363, 91630204, and 51661135011), the Fundamental Research Funds for the Central Universities (Grant No. 20720180003), and NSF of Fujian Province of China (No.2018J01004). Shuyu Sun acknowledges that the research reported in this publication was supported in part by funding from King Abdullah University of Science and Technology (KAUST) through grants BAS/1/1351-01, URF/1/2993-01, and REP/1/2879-01.
dc.publisherElsevier BV
dc.relation.urlhttps://linkinghub.elsevier.com/retrieve/pii/S0307904X20301153
dc.relation.urlhttp://arxiv.org/pdf/1801.08739
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Applied Mathematical Modelling. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Applied Mathematical Modelling, [83, , (2020-03-04)] DOI: 10.1016/j.apm.2020.02.022 . © 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.titleFully discrete energy stable scheme for a phase-field moving contact line model with variable densities and viscosities
dc.typeArticle
dc.contributor.departmentComputational Transport Phenomena Lab
dc.contributor.departmentEarth Science and Engineering Program
dc.contributor.departmentPhysical Science and Engineering (PSE) Division
dc.identifier.journalApplied Mathematical Modelling
dc.rights.embargodate2022-04-02
dc.eprint.versionPost-print
dc.contributor.institutionResearch Center of Multiphase Flow in Porous Media, School of Petroleum Engineering, China University of Petroleum (East China), Qingdao 266580, China
dc.contributor.institutionSchool of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University, Xiamen 361005, China
dc.identifier.volume83
dc.identifier.pages614-639
dc.identifier.arxividarXiv:1801.08739
kaust.personSun, Shuyu
kaust.grant.numberBAS/1/1351-01
kaust.grant.numberREP/1/2879-01
kaust.grant.numberURF/1/2993-01
dc.date.accepted2020-02-25
dc.identifier.eid2-s2.0-85082667333
refterms.dateFOA2018-06-13T16:22:01Z


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