Modelling of Eulerian incompressible fluid flows by using peridynamic differential operator

Nguyen, Cong Tien and Oterkus, Selda and Oterkus, Erkan and Amin, Islam and Ozdemir, Murat and El-Aassar, Abdel-Hameed and Shawky, Hosam (2021) Modelling of Eulerian incompressible fluid flows by using peridynamic differential operator. Ocean Engineering, 239. 109815. ISSN 0029-8018 (https://doi.org/10.1016/j.oceaneng.2021.109815)

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Abstract

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.

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