Stability and accuracy of the weakly compressible SPH with particle regularization techniques

Abstract

This paper proposes and validates two new particle regularization techniques for the Smoothed Particle Hydrodynamics (SPH) numerical method to improve its stability and accuracy for free surface flow simulations. We introduce a general form of the Dynamic pair-wise Particle Collision (DPC) regularization technique that we recently proposed in the context of the Moving Particle Semi-implicit (MPS) method in Jandaghian et al. (2021). The DPC coupled with the standard Particle Shifting (PS) technique has given rise to a hybrid approach that we propose to alleviate particle clustering issues in the free-surface and splashed regions. We validate the proposed techniques to four benchmark cases: (i) the oscillating droplet, (ii) the two-dimensional water dam-break, (iii) the two-dimensional water sloshing, and (iv) the three-dimensional water dam break against a rigid obstacle. We evaluate their impacts on the stability, accuracy and the conservation properties of the test cases. The qualitative and quantitative analysis of the results shows that despite its simplicity, the DPC technique is more effective in reducing the spatial disorder and capturing the impact events compared with the standard and the newly improved hybrid PS methods. Although the hybrid PS technique improves particle distribution at the free surface, it still suffers from the inconsistent implementation of the PS equation which unphysically increases the fluid volume and violates the conservation of potential energy in the long-term simulations. Overall, the conservative DPC algorithm proves to be a simple and efficient alternative regularization technique for simulating such highly dynamic free-surface flows.