Crank–Nicolson Leap-Frog Time Stepping Decoupled Scheme for the Fluid–Fluid Interaction Problems

Abstract

A fully discrete Crank-Nicolson leap-frog time stepping decoupled (CNLFD) scheme is presented and studied for the fluid–fluid interaction problems. The proposed scheme deals with the spatial discretization by finite element method (FEM), treats the temporal discretization by CNLF scheme and decouples the nonlinear interface condition by using a geometric averaging of the jump. The unconditional stability and error estimate are proven. Numerical tests are performed to demonstrate the robustness of this method.

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Acknowledgements

The authors sincerely thank the anonymous reviewers and editor for their helpful suggestions.

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Correspondence to Yinnian He.

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This work is in part supported by the NSF of China (Nos. 11861054, U19A2079, 11671345 and 11771348)), Scientific research starting foundation for the high level talents of shihezi university (No. RCSX201732) and the Xinjiang Provincial University Research Foundation of China (No. XJEDU2020I001, XJEDU2020Y001).

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Qian, L., Feng, X. & He, Y. Crank–Nicolson Leap-Frog Time Stepping Decoupled Scheme for the Fluid–Fluid Interaction Problems. J Sci Comput 84, 4 (2020). https://doi.org/10.1007/s10915-020-01254-5

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Keywords

  • Fluid–fluid interaction problems
  • Nonlinear interface condition
  • Crank-Nicolson leap-frog
  • Decoupled scheme
  • Stability analysis

Mathematics Subject Classification

  • 65N12
  • 65N30
  • 65M15
  • 65M60