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The Exponential SAV Approach for the Time-Fractional Allen–Cahn and Cahn–Hilliard Phase-Field Models

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Abstract

In this paper, we take a consideration of a class of time-fractional phase-field models including the Allen–Cahn and Cahn–Hilliard equations. Based on the exponential scalar auxiliary variable (ESAV) approach, we construct two explicit time-stepping schemes, in which the fractional derivative is discretized by L1 and \(L1+\) formulas respectively. It is worth to mentioning that our novel schemes are effective for the completely decoupled computations of the phase variable \(\phi \) and the auxiliary variable R. In fact, the above two schemes admit energy dissipation law on general nonuniform meshes, which is inherent property in the continuous level. Finally, several numerical experiments are carried out to verify the accuracy and efficiency of our proposed methods.

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Acknowledgements

The authors would like to express their sincere thanks to Prof. Tao Zhou (from Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences) for his very helpful suggestions. Meanwhile, the authors would like to express their sincere thanks to the editor and the reviewers for their very helpful comments and suggestions, which greatly improved the quality of this paper.

Funding

Funding is provided by Fundamental Research Funds for the Central Universities (Grant No. 22CX03020A).

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Authors and Affiliations

  1. Department of Applied Mathematics, China University of Petroleum, Qingdao, 266580, People’s Republic of China

    Yue Yu, Jiansong Zhang & Rong Qin

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  1. Yue Yu
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  2. Jiansong Zhang
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Correspondence to Jiansong Zhang.

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Yu, Y., Zhang, J. & Qin, R. The Exponential SAV Approach for the Time-Fractional Allen–Cahn and Cahn–Hilliard Phase-Field Models. J Sci Comput 94, 33 (2023). https://doi.org/10.1007/s10915-022-02085-2

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  • DOI: https://doi.org/10.1007/s10915-022-02085-2

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