Improved Incompressible Smoothed Particle Hydrodynamics method for simulating flow around bluff bodies

Abstract

In this article, we present numerical solutions for flow over an airfoil and a square obstacle using Incompressible Smoothed Particle Hydrodynamics (ISPH) method with an improved solid boundary treatment approach, referred to as the Multiple Boundary Tangents (MBT) method. It was shown that the MBT boundary treatment technique is very effective for tackling boundaries of complex shapes. Also, we have proposed the usage of the repulsive component of the Lennard-Jones Potential (LJP) in the advection equation to repair particle fractures occurring in the SPH method due to the tendency of SPH particles to follow the stream line trajectory. This approach is named as the artificial particle displacement method. Numerical results suggest that the improved ISPH method which is consisting of the MBT method, artificial particle displacement and the corrective SPH discretization scheme enables one to obtain very stable and robust SPH simulations. The square obstacle and NACA airfoil geometry with the angle of attacks between 0° and 15° were simulated in a laminar flow field with relatively high Reynolds numbers. We illustrated that the improved ISPH method is able to capture the complex physics of bluff-body flows naturally such as the flow separation, wake formation at the trailing edge, and the vortex shedding. The SPH results are validated with a mesh-dependent Finite Element Method (FEM) and excellent agreements among the results were observed.