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A BDF2 energy stable scheme for the binary fluid-surfactant hydrodynamic model
  • Yuzhe Qin,
  • Rui Chen,
  • Zhengru Zhang
Yuzhe Qin
Beijing Normal University
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Rui Chen
Beijing University of Posts and Telecommunications
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Zhengru Zhang
Beijing Normal University
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A second-order time stepping scheme is developed for the binary fluid-surfactant phase field model coupled with hydrodynamics by using the scalar auxiliary variable approach and pressure correction method. The free energy contains a double-well potential, a nonlinear coupling entropy and a Flory-Huggins potential. By introducing one scalar auxiliary variable, the system is transformed into an equivalent form so that the nonlinear terms can be treated semi-explicitly. The scheme is linear and decoupled; thus, they can be solved eciently. We further prove that the semidiscretized scheme in time is unconditionally energy stable. Numerical experiments are performed to validate the accuracy and energy stability of the proposed scheme.

Peer review status:IN REVISION

12 Nov 2020Submitted to Mathematical Methods in the Applied Sciences
13 Nov 2020Submission Checks Completed
13 Nov 2020Assigned to Editor
09 Feb 2021Reviewer(s) Assigned
26 Apr 2021Review(s) Completed, Editorial Evaluation Pending
26 Apr 2021Editorial Decision: Revise Minor
13 May 20211st Revision Received
13 May 2021Assigned to Editor
13 May 2021Submission Checks Completed