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Volume 25, Issue 3
On Linear and Unconditionally Energy Stable Algorithms for Variable Mobility Cahn-Hilliard Type Equation with Logarithmic Flory-Huggins Potential

Xiaofeng Yang & Jia Zhao

DOI: 10.4208/cicp.OA-2017-0259

Commun. Comput. Phys., 25 (2019), pp. 703-728.

Published online: 2018-11

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  • Abstract

In this paper, we consider numerical approximations for the fourth-order Cahn-Hilliard equation with the concentration-dependent mobility and the logarithmic Flory-Huggins bulk potential. One numerical challenge in solving such system is how to develop proper temporal discretization for nonlinear terms in order to preserve its energy stability at the time-discrete level. We overcome it by developing a set of first and second order time marching schemes based on a newly developed "Invariant Energy Quadratization" approach. Its novelty is producing linear schemes, by discretizing all nonlinear terms semi-explicitly. We further rigorously prove all proposed schemes are unconditionally energy stable. Various 2D and 3D numerical simulations are presented to demonstrate the stability, accuracy, and efficiency of the proposed schemes thereafter.

  • Keywords

Phase-field, linear, Cahn-Hilliard, stability, variable mobility, Flory-Huggins.

  • AMS Subject Headings

65N12, 65P40, 65Z05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-25-703, author = {Xiaofeng Yang and Jia Zhao}, title = {On Linear and Unconditionally Energy Stable Algorithms for Variable Mobility Cahn-Hilliard Type Equation with Logarithmic Flory-Huggins Potential}, journal = {Communications in Computational Physics}, year = {2018}, volume = {25}, number = {3}, pages = {703--728}, abstract = {

In this paper, we consider numerical approximations for the fourth-order Cahn-Hilliard equation with the concentration-dependent mobility and the logarithmic Flory-Huggins bulk potential. One numerical challenge in solving such system is how to develop proper temporal discretization for nonlinear terms in order to preserve its energy stability at the time-discrete level. We overcome it by developing a set of first and second order time marching schemes based on a newly developed "Invariant Energy Quadratization" approach. Its novelty is producing linear schemes, by discretizing all nonlinear terms semi-explicitly. We further rigorously prove all proposed schemes are unconditionally energy stable. Various 2D and 3D numerical simulations are presented to demonstrate the stability, accuracy, and efficiency of the proposed schemes thereafter.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0259}, url = {http://global-sci.org/intro/article_detail/cicp/12826.html} }
TY - JOUR T1 - On Linear and Unconditionally Energy Stable Algorithms for Variable Mobility Cahn-Hilliard Type Equation with Logarithmic Flory-Huggins Potential AU - Xiaofeng Yang & Jia Zhao JO - Communications in Computational Physics VL - 3 SP - 703 EP - 728 PY - 2018 DA - 2018/11 SN - 25 DO - http://doi.org/10.4208/cicp.OA-2017-0259 UR - https://global-sci.org/intro/article_detail/cicp/12826.html KW - Phase-field, linear, Cahn-Hilliard, stability, variable mobility, Flory-Huggins. AB -

In this paper, we consider numerical approximations for the fourth-order Cahn-Hilliard equation with the concentration-dependent mobility and the logarithmic Flory-Huggins bulk potential. One numerical challenge in solving such system is how to develop proper temporal discretization for nonlinear terms in order to preserve its energy stability at the time-discrete level. We overcome it by developing a set of first and second order time marching schemes based on a newly developed "Invariant Energy Quadratization" approach. Its novelty is producing linear schemes, by discretizing all nonlinear terms semi-explicitly. We further rigorously prove all proposed schemes are unconditionally energy stable. Various 2D and 3D numerical simulations are presented to demonstrate the stability, accuracy, and efficiency of the proposed schemes thereafter.

Xiaofeng Yang and Jia Zhao. (2018). On Linear and Unconditionally Energy Stable Algorithms for Variable Mobility Cahn-Hilliard Type Equation with Logarithmic Flory-Huggins Potential. Communications in Computational Physics. 25 (3). 703-728. doi:10.4208/cicp.OA-2017-0259
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