Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 290, Issue -, Pages 139-156Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2015.02.046
Keywords
Cahn-Hilliard-Navier-Stokes; Diffuse interface model; Energy law preserving; Unique solvability; Pressure-projection; Mixed finite element
Funding
- NSF Grant [DMS1312701, DMS1008852]
- Florida State University
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1312701] Funding Source: National Science Foundation
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We propose a novel second order in time numerical scheme for Cahn-Hilliard-Navier-Stokes phase field model with matched density. The scheme is based on second order convex-splitting for the Cahn-Hilliard equation and pressure-projection for the Navier-Stokes equation. We show that the scheme is mass-conservative, satisfies a modified energy law and is therefore unconditionally stable. Moreover, we prove that the scheme is unconditionally uniquely solvable at each time step by exploring the monotonicity associated with the scheme. Thanks to the simple coupling of the scheme, we design an efficient Picard iteration procedure to further decouple the computation of Cahn-Hilliard equation and Navier-Stokes equation. We implement the scheme by the mixed finite element method. Ample numerical experiments are performed to validate the accuracy and efficiency of the numerical scheme. (C) 2015 Elsevier Inc. All rights reserved.
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