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Abstract
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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.
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