Eulerian ISPH Method for Simulating Internal Flows

Abstract

In this article the possibility to use Eulerian approach in the conventional ISPH method in simulation of internal fluid flows is studied. The use of Eulerian approach makes it possible to use non-uniform particle distributions to increase the resolution in the sensitive parts of the domain, different boundary conditions can be employed more freely and particle penetration in the solid walls and tensile instability no longer require elaborate procedures. The governing equations are solved in an Eulerian framework containing both the temporal and local derivatives which make the momentum equations non-linear. Some special treatment and smaller time steps are required to remedy this non-linearity of the problem. In this study, projection method is used to enforce incompressibility with the evaluation of an intermediate velocity and then this velocity is projected on the divergence-free space. This method is applied to the internal fluid flows in a shear-driven cavity, Couette flow, a flow inside a duct with variable area and flow around a circular cylinder within a constant area duct. The results are compared with the results of Lagrangian ISPH and WCSPH methods as well as finite volume and Lattice Boltzmann grid based schemes. The results of the studied scheme have the same accuracy for velocity field and have better accuracy in pressure distribution than ISPH and WCSPH methods. Non-uniform particle distributions are also studied to check the applicability of this method and Good agreement is also observed between uniform and non-uniform particle distributions.

Keywords

• Eulerian; Smoothed particle hydrodynamics; Meshfree; Incompressible flow.