Modelling of Eulerian incompressible fluid flows by using peridynamic differential operator

Cong Tien Nguyen, Selda Oterkus, Erkan Oterkus, Islam Amin, Murat Ozdemir, Abdel-Hameed El-Aassar, Hosam Shawky

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This study presents a novel method for modelling of Eulerian incompressible fluid flow by using peridynamic differential operator. The peridynamic differential operator is used to calculate partial derivatives in the Navier-Stokes equations. The pressure Poisson equation is used to obtain the pressure field whereas the velocity field is obtained by solving momentum equations. The numerical procedure to solve Navier-Stokes equations in peridynamics for the incompressible fluid is also provided. The capability of the proposed peridynamic incompressible fluid model is demonstrated by considering problems of two-dimensional cavitation, a flow inside an open channel, and a flow over a cylinder. Moreover, to demonstrate the capabilities of the proposed model, the problems of two-dimensional cavitation and a flow over a cylinder are investigated for different Reynolds numbers. The vortex shedding is also captured for the problem of a flow over a cylinder at Reynolds number of 푅푒 = 100. For verification purposes, the peridynamic results are compared with the results obtained by ANSYS Fluent, a commercial fluid dynamics software.
Original languageEnglish
Number of pages55
JournalOcean Engineering
Publication statusAccepted/In press - 5 Sep 2021


  • peridynamics
  • peridynamic differential operators
  • incompressible fluid
  • Eulerian approach
  • vortex shedding


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