Towards Industrial Application of Smoothed Particle Hydrodynamics: A Localized Implicit Iterative Particle Shifting Approach

Meshless methods such as Smoothed Particle Hydrodynamics (SPH) suffer from particle distribution irregularities caused by Lagrangian particle motion, which degrades the accuracy and stability of the numerical scheme. While Particle Shifting Techniques (PSTs) have been developed to mitigate this, existing explicit shifting methods lack the ability to enforce strict particle uniformity. Conversely, implicit iterative shifting techniques that can provide a globally uniform particle distribution are often computationally demanding for large-scale applications. This thesis advances the state of the art by introducing a Novel Implicit Iterative Particle Shifting (NIIPS) formulation. NIIPS minimizes the gradient of particle concentration by solving a system of linear equations and stabilizes the shifting procedure by incorporating neighboring particle effects. Moreover, a parallelization strategy for the linear system construction and its solution is proposed, which ensures efficiency for handling large-scale simulations and industrial applications. To further optimize the computational cost and memory usage, a Localized NIIPS (L-NIIPS) method is developed, which applies shifting only in non-uniform regions while limiting the shifting magnitude to improve accuracy. As a baseline assessment, comprehensive 2D benchmark tests within the standard Weakly Compressible SPH (WCSPH) framework were performed using the Taylor-Green Vortex (TGV), moving square box, oscillating droplet, and the dam break. The results showed the efficiency of both NIIPS and L-NIIPS in achieving uniform particle distributions compared to existing shifting techniques. In particular, L-NIIPS achieved optimal performance at an affordable computational cost, effectively ensuring numerical accuracy and particle uniformity, even in the vicinity of the free surface. Subsequently, the L-NIIPS approach was integrated into ANDRITZ Hydro’s in-house solver, ASPHODEL, which employs an Arbitrary Lagrangian-Eulerian SPH (ALE-SPH) solver. To account for shifting-induced advection, an Advection Correction Step (ACS) formulation is introduced and further refined in the presence of wall boundaries to maintain the consistency of the numerical scheme. Finally, the L-NIIPS together with ACS were validated across benchmark cases, including 2D Taylor-Green Vortex, moving square box, 2D/3D impinging jet, and the demanding 3D Pelton bucket. The results demonstrated the capability of the proposed methodologies in free-surface flows and large-scale simulations, providing highly uniform particle distribution, minimal numerical error, and smooth pressure fields at a reasonable computational cost.