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A Decoupled Energy Stable Adaptive Finite Element Method for Cahn–Hilliard–Navier–Stokes Equations

A Decoupled Energy Stable Adaptive Finite Element Method for Cahn–Hilliard–Navier–Stokes Equations
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Year:    2021

Author:    Yaoyao Chen, Yunqing Huang, Nianyu Yi

Communications in Computational Physics, Vol. 29 (2021), Iss. 4 : pp. 1186–1212

Abstract

In this paper, we propose, analyze, and numerically validate an adaptive finite element method for the Cahn–Hilliard–Navier–Stokes equations. The adaptive method is based on a linear, decoupled scheme introduced by Shen and Yang [30]. An unconditionally energy stable discrete law for the modified energy is shown for the fully discrete scheme. A superconvergent cluster recovery based a posteriori error estimations are constructed for both the phase field variable and velocity field function, respectively. Based on the proposed space and time discretization error estimators, a time-space adaptive algorithm is designed for numerical approximation of the Cahn–Hilliard–Navier–Stokes equations. Numerical experiments are presented to illustrate the reliability and efficiency of the proposed error estimators and the corresponding adaptive algorithm.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2020-0032

Communications in Computational Physics, Vol. 29 (2021), Iss. 4 : pp. 1186–1212

Published online:    2021-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    27

Keywords:    Cahn–Hilliard equation Navier–Stokes equation energy stability adaptive SCR.

Author Details

Yaoyao Chen

Yunqing Huang

Nianyu Yi

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