A second order in time, uniquely solvable, unconditionally stable numerical scheme for Cahn-Hilliard-Navier-Stokes equation

JOURNAL OF COMPUTATIONAL PHYSICS

卷:290

Article

Han, Daozhi¹  Wang, Xiaoming¹ 

[1] Florida State Univ, Dept Math, Tallahassee, FL 32306 USA

关键词: Cahn-Hilliard-Navier-Stokes;    Diffuse interface model;    Energy law preserving;    Unique solvability;    Pressure-projection;    Mixed finite element;   

DOI  :  10.1016/j.jcp.2015.02.046

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

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