ALE–SPH formulation with 3D parallel localized implicit iterative particle shifting: from particle regularity to industrial applications

This paper presents a three-dimensional formulation of the Localized Novel Implicit Iterative Particle Shifting (L-NIIPS) method within the Arbitrary Lagrangian–Eulerian Smoothed Particle Hydrodynamics (ALE-SPH) framework to minimize particle concentration gradients, thereby improving the regularity of the particle distribution. A multi-node parallelization approach is introduced for the L-NIIPS approach to efficiently handle complex 3D cases. The methodology also incorporates wall contribution terms into the Advection Correction Step (ACS) formulation to ensure consistent transport of physical quantities through the boundary integral method, thereby eliminating pressure oscillations near solid boundaries and yielding noise-free pressure fields. Through numerical evaluation, optimal L-NIIPS parameters are identified that strike a balance among accuracy, computational cost, and particle distribution regularity, proving robust across different flow configurations and eliminating the need for case-specific tuning. Validation is performed using established SPH benchmarks, including the Taylor–Green Vortex (TGV), moving square box, and 2D/3D impinging jets on a flat plate and further assessed through a demanding 3D Pelton bucket simulation. Results confirm that the proposed methodology significantly enhances accuracy and smoothness of the physical fields while maintaining a manageable computational overhead, making it suitable for industrial applications.