An energy stable C<sup>0</sup> finite element scheme for a quasi-incompressible phase-field model of moving contact line with variable density

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In this paper, we focus on modeling and simulation of two-phase flow problems with moving contact lines and variable density. A thermodynamically consistent phase-field model with general Navier boundary condition is developed based on the concept of quasi-incompressibility and the energy variational method. A mass conserving C0 finite element scheme is proposed to solve the PDE system. Energy stability is achieved at the fully discrete level. Various numerical results confirm that the proposed scheme for both P1 element and P2 element are energy stable.





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Shen, L, H Huang, P Lin, Z Song and S Xu (2020). An energy stable C0 finite element scheme for a quasi-incompressible phase-field model of moving contact line with variable density. Journal of Computational Physics, 405. pp. 109179–109179. 10.1016/ Retrieved from

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Shixin Xu

Assistant Professor of Mathematics at Duke Kunshan University

Shixin Xu is an Assistant Professor of Mathematics.   His research interests are machine learning and data-driven models for diseases,  multiscale modeling of complex fluids, Neurovascular coupling, homogenization theory, and numerical analysis.  The current projects he is working on are

  • image data-based for the prediction of hemorrhagic transformation in acute ischemic stroke,
  • electrodynamics modeling of saltatory conduction along a myelinated axon
  • electrochemical modeling
  • fluid-structure interaction with mass transportation and reaction

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