A decoupled finite element method for fluid–fluid interaction
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Wei Li
and
Yinnian He
Abstract
A decoupled finite element method based on the scalar auxiliary variable and vector penalty projection approach is constructed and analysed for solving a fluid–fluid interaction problem, which includes two Navier–Stokes equations coupled by some nonlinear interface conditions. The proposed full-discrete scheme is a combination of mixed finite element approximation for spatial discretization, backward Euler scheme for temporal discretization, as well as explicit treatment for the interface conditions, and can penalize for lack of mass conservation. Furthermore, unconditional energy stability is given and error estimates for the fully discrete scheme are showed. Finally, some numerical experiments are provided to illustrate the theoretical results and efficiency of the presented method.
Acknowledgements
The authors would like to thank the editor and anonymous referees, whose helpful comments led to an improved version of the presented results.
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Research funding: This work is sponsored by the Natural Science Foundation of China (grant No. 12361077), the Natural Science Foundation of Xinjiang Uygur Autonomous Region (grant No. 2023D14014) and Tianshan Talent Training Program of Xinjiang Uygur Autonomous Region (grant No. 2023TSYCCX0103).
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