In this work, we present solutions for flow over an airfoil and square obstacle using Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) method. For the solution of these two problems, we present an improved WCSPH algorithm that can handle complex geometries with the usage of multiple tangent solid boundary method, and eliminate particle clustering induced instabilities with the implementation of particle fracture repair procedure as well as the corrected SPH discretization scheme. We have shown that the improved WCSPH method can be effectively used for flow simulations over bluff-bodies with Reynolds numbers as high as 1400, which is not achievable with standard WCSPH formulations. Our simulation results are validated with a Finite Element mesh-dependent Method (FEM), and excellent agreements among the results were observed. We illustrated that the improved WCSPH method is able to capture the complex physics of bluff-body flows naturally such as flow separation, detachment of separated flow, wake formation at the trailing edge, and vortex shedding without any extra effort to increase the particle resolution in some specific areas of interest.

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