Localized implicit iterative shifting to improve particle distribution in Smoothed Particle Hydrodynamics

This study presents a novel Implicit Iterative Particle Shifting method designed to enhance the accuracy of Smoothed Particle Hydrodynamics (SPH) simulations by improving particle distribution through the solution of a linear system of equations. The proposed approach addresses key limitations of existing techniques, namely distribution instability and lack of control over maximum particle displacement by accounting for the contribution of neighboring particles on a given particle when constructing the linear system. The method also imposes a constraint on the shifting magnitude, allowing for better control of particle movement and improved distribution stability also in presence of free surface. To reduce computational cost, a localization procedure has been introduced that restricts particle shifting to regions where it is necessary. The effectiveness of the method is demonstrated through a series of benchmark tests, including the Taylor-Green vortex, a moving square box, an oscillating droplet, and a dam break flow. The results show substantial improvements in the uniformity of the particle distribution, computational efficiency, and simulation accuracy compared to established methods.