Multi-phase fluid flow simulation by using peridynamic differential operator

Yan Gao, Selda Oterkus

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The problems of multi-phase fluid flows are often encountered in engineering. In this study, a non-local numerical model of multi-phase fluid flows in the Lagrangian description is developed. Based on the peridynamic theory, a peridynamic differential operator is proposed which can convert any arbitrary order of differentials into their integral form without calculating the peridynamic parameters. Therefore, the Navier-Stokes equations including the surface tension forces are reformulated into their integral form. Subsequently, an updated Lagrangian algorithm for solving the multi-phase fluid flow problems is proposed. Besides, the particle shifting technology and moving least square algorithm are also adopted to avoid the possible tension instability. Finally, several benchmark multi-phase fluid flow problems such as two-phase hydrostatic problem, two-phase Poiseuille flow, and 2D square droplet deformation are solved to validate the proposed non-local model. It can be concluded from the current study that the peridynamic differential operator can be applied as an alternative method for multi-phase fluid flow simulation.
Original languageEnglish
JournalOcean Engineering
Publication statusAccepted/In press - 7 Sep 2020


  • peridynamic differential operator
  • non-local model
  • multi-phase flows
  • N-S equations
  • surface tension force

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