Rapid Variable Resolution Particle Initialization for Complex Geometries

TL;DR

The paper tackles the challenge of generating high-quality, boundary-conforming particle distributions for meshless SPH simulations with adaptive resolution and simultaneous solid–fluid initialization. It introduces a modular framework built on five components—restoring force, particle shifting, volume adaptivity, mass dissipation, and interface handling—implemented with three particle sets and an explicit treatment of interfaces. Across 2D and 3D test cases, the method delivers low density variation, small kernel-gradient sums, and favorable spatial disorder, while achieving substantial speedups over prior approaches and enabling complex geometries to be simulated efficiently. Limitations include reliance on a constant density assumption, sensitivity to interface proximity to frozen particles, STL watertightness, and the use of a global time step; future work points to local adaptive time stepping and further performance optimizations. Overall, the approach offers a practical, building-blocks-based solution for automated, high-quality particle initialization in meshless simulations, with clear potential for integration into existing SPH workflows.

Abstract

The accuracy of meshless methods like Smoothed Particle Hydrodynamics (SPH) is highly dependent on the quality of the particle distribution. Existing particle initialization techniques often struggle to simultaneously achieve adaptive resolution, handle intricate boundaries, and efficiently generate well-packed distributions inside and outside a boundary. This work presents a fast and robust particle initialization method that achieves these goals using standard SPH building blocks. Our approach enables simultaneous initialization of fluid and solid regions, supports arbitrary geometries, and achieves high-quality, quasi-uniform particle arrangements without complex procedures like surface bonding. Extensive results in both 2D and 3D demonstrate that the obtained particle distributions exhibit good boundary conformity, low spatial disorder, and minimal density variation, all with significantly reduced computational cost compared to existing approaches. This work paves the way for automated particle initialization to accurately model flow in and around bodies with meshless methods, particularly with SPH.

Figures (35)

• Figure 1: Particle sets used in the method. The blue circles represent free particles, the red diamonds represent interface particles, and the black squares represent frozen particles.
• Figure 2: Splitting pattern in 2D (left) and 3D (right). The grey parent particle is split into four offspring particles in 2D and eight offspring particles in 3D. The offspring particles are teal colored.
• Figure 3: Particle initialization without interface, initial configuration is on the left and the final configuration is coloured by $\rho$ is on the right.
• Figure 4: Particle initialization around a hexagon, initial configuration is on the left and the final configuration is coloured by $\rho$ is on the right.
• Figure 5: Particle initialization of a circle with constant resolution, coloured by $\rho$ (left) and $\left|\left|\nabla \Gamma\right|\right|_2$ (right). The plot on the left shows the complete domain with the frozen particles in red.