Modelling of Eulerian incompressible fluid flows by using peridynamic differential operator

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 Re=100. For verification purposes, the peridynamic results are compared with the results obtained by ANSYS Fluent, a commercial fluid dynamics software.