Title

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.

Department(s)

Mathematics and Statistics

Comments

D. Han is supported by the U.S. National Science Foundation via DMS-1912715

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

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