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A Linear Unconditionally Stable Scheme for the Incompressible Cahn–Hilliard–Navier–Stokes Phase-Field Model


In this paper, we propose a linear, unconditional energy-stable time-discretization scheme for Cahn–Hilliard–Navier–Stokes model, which is a phase-field model for two-phase incompressible flow. Based on a Lagrange multiplier approach and pressure projection method, our proposed scheme is linearized. Error analyses are carried out under the finite element frame; numerical experiments are done to demonstrate the effectiveness for the proposed scheme.

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Correspondence to Hongen Jia.

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Supported by the National Nature Foundation of China (No. 11872264), the Provincial Natural Science Foundation of Shanxi (No. 201901D111123), Scientific and Technologial Innovation Programs of Higher Education Institutions in Shanxi (No. 2017119), Key Research and Development (R&D) Projects of Shanxi Province (No. 201903D121038).

Communicated by Davoud Mirzaei.

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Wang, X., Li, K. & Jia, H. A Linear Unconditionally Stable Scheme for the Incompressible Cahn–Hilliard–Navier–Stokes Phase-Field Model. Bull. Iran. Math. Soc. (2021).

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  • Phase-field
  • Two-phase incompressible flow
  • Navier–Stokes
  • Lagrange multiplier approach

Mathematics Subject Classification

  • 35Q30
  • 74S05