Robust and efficient pre-processing techniques for particle-based methods including dynamic boundary generation

TL;DR

A preprocessing technique for 2D and 3D geometries, optimized for smoothed particle hydrodynamics (SPH) and other particle-based methods, is introduced, which is robust to imperfect input geometries and memory-efficient without compromising performance.

Abstract

Obtaining high-quality particle distributions for stable and accurate particle-based simulations poses significant challenges, especially for complex geometries. We introduce a preprocessing technique for 2D and 3D geometries, optimized for smoothed particle hydrodynamics (SPH) and other particle-based methods. Our pipeline begins with the generation of a resolution-adaptive point cloud near the geometry's surface employing a face-based neighborhood search. This point cloud forms the basis for a signed distance field, enabling efficient, localized computations near surface regions. To create an initial particle configuration, we apply a hierarchical winding number method for fast and accurate inside-outside segmentation. Particle positions are then relaxed using an SPH-inspired scheme, which also serves to pack boundary particles. This ensures full kernel support and promotes isotropic distributions while preserving the geometry interface. By leveraging the meshless nature of particle-based methods, our approach does not require connectivity information and is thus straightforward to integrate into existing particle-based frameworks. It is robust to imperfect input geometries and memory-efficient without compromising performance. Moreover, our experiments demonstrate that with increasingly higher resolution, the resulting particle distribution converges to the exact geometry.

Figures (30)

• Figure 1: (a) visualization of the polygonal traversal of an arbitrary geometry surface. (b) point grid surrounding the geometry's surface, where the points store the signed distances to the surface, visualized as a color map. (c) and (d) show the initial configuration of the boundary and interior particles, respectively.
• Figure 2: (a) shows the grid structure of the initial configuration, which does not accurately represent the geometry surface. (b) displays the final configuration of the particles, which are isotropically distributed while accurately preserving the geometry surface.
• Figure 3: Interpolation of the SDF onto the particles (black dots), where the dashed circles represent the compact support of the kernel. The SDF is shown with colored points. The solid black line represents the geometry. The dashed-dotted lines represent the thickness of the convex hull of the point cloud.
• Figure 4: Two exemplary edges (blue and red) in cell grids, each with a different search radius $r_s$, where $\Delta x$ is the particle spacing. The grey edges are part of the polygon traversal but not considered in this example. The bounding boxes of the edges are framed with the corresponding color. The dashed boxes represent the direct neighbor cells of the bounding boxes.
• Figure 5: Signed distance point cloud for different resolutions with a maximum signed distance of $4\Delta x$ requiring a search radius of $r_s = 4\Delta x$. The geometry surface is represented by the black solid line. Top: $\Delta x = 0.015$, bottom: $\Delta x = 0.01$.