A Linear Second-Order in Time Unconditionally Energy Stable Finite Element Scheme for a Cahn-Hilliard Phase-Field Model for Two-Phase Incompressible Flow of Variable Densities
Abstract
We propose a novel second-order BDF time stepping method of variable time step sizes combined with a classical residual-based stabilized finite element spatial discretization using the Streameline-Upwind Petrov-Galerkin (SUPG)/pressure stabilization Petrov-Galerkin (PSPG)/grad-div stabilization for solving the phase-field model for two-phase incompressible flow of different densities and viscosities in the advection dominated regime. In the case of uniform time step size and without extra stabilization, the scheme is shown to satisfy a discrete energy law. Benchmark test of the Rayleigh-Taylor instability under high Reynolds number and Péclect number demonstrates that the scheme captures details of the instability comparable to results in the literature by schemes based on sharp-interface models.
Recommended Citation
G. Fu and D. Han, "A Linear Second-Order in Time Unconditionally Energy Stable Finite Element Scheme for a Cahn-Hilliard Phase-Field Model for Two-Phase Incompressible Flow of Variable Densities," Computer Methods in Applied Mechanics and Engineering, vol. 387, article no. 114186, Elsevier, Dec 2021.
The definitive version is available at https://doi.org/10.1016/j.cma.2021.114186
Department(s)
Mathematics and Statistics
Keywords and Phrases
Cahn-Hilliard-Navier-Stokes; Energy Law Preserving; Stabilized Finite Element Method; Two-Phase Incompressible Flow
International Standard Serial Number (ISSN)
0045-7825
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2021 Elsevier, All rights reserved.
Publication Date
15 Dec 2021
Comments
D. Han is supported by the U.S. National Science Foundation via DMS-1912715