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An efficient and energy stable scheme for a phase‐field model for the moving contact line problem
Author(s) -
Aland Sebastian,
Chen Feng
Publication year - 2015
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4200
Subject(s) - discretization , energy (signal processing) , scheme (mathematics) , phase field models , mathematics , stability (learning theory) , finite element method , line (geometry) , property (philosophy) , boundary value problem , field (mathematics) , boundary (topology) , mathematical optimization , mathematical analysis , phase (matter) , computer science , geometry , physics , philosophy , statistics , epistemology , quantum mechanics , machine learning , pure mathematics , thermodynamics
Summary In this paper, we propose for the first time a linearly coupled, energy stable scheme for the Navier–Stokes–Cahn–Hilliard system with generalized Navier boundary condition. We rigorously prove the unconditional energy stability for the proposed time discretization as well as for a fully discrete finite element scheme. Using numerical tests, we verify the accuracy, confirm the decreasing property of the discrete energy, and demonstrate the effectiveness of our method through numerical simulations in both 2‐D and 3‐D. Copyright © 2015 John Wiley & Sons, Ltd.