Rouhollah Fatehi

‎Incompressibility is a challenge in the context of Smoothed Particle Hydrodynamics (SPH)‎. ‎There are two major approaches to handle the Incompressibility; weakly compressible and fully incompressible SPH methods‎. ‎In the present work‎, ‎a SPH method based on the augmented Lagrangian method is proposed‎. ‎In this method‎, ‎it is assumed that the density is constant‎. ‎However‎, ‎the pressure is obtained from an equation of state‎. ‎To achieve the divergence-free velocity field‎, ‎the calculation of velocity and pressure are repeated iteratively‎. ‎So‎, ‎it is categorized as density-based method‎. ‎Here‎, ‎a new augmented Lagrangian SPH method is developed and the results are compared with those of a recent modified version of the weakly compressible SPH method in two illustrative 1D and 2D incompressible flow problems‎. ‎It has been observed that the results of the proposed method overcome the pressure oscillations much better in comparison with those of the weakly compressible method‎.