An implementation of smoothed particle hydrodynamic methods for fluids problems

In this article, we present a numerical method that is Smoothed Particle Hydrodynamic (SPH) method. In the SPH method for the Navier - Stokes equations the most widespread method to solve for pressure and mass conservation is the weakly compressible assumption (WCSPH). This article presents two important benchmark problems to validate the algorithm of SPH method. The two benchmark problems chosen are the Lid - driven cavity problem and Poiseuille flow problem at very low Reynolds numbers. The SPH results are also in good agreement with the analytical solution