Algorithms for uniform particle initialization in domains with complex boundaries

Accurate mesh-free simulation of fluid flows involving complex boundaries requires that the boundaries be captured accurately in terms of particles. In the context of incompressible/weakly-compressible fluid flow, the SPH method is more accurate when the particle distribution is uniform. Hence, for time-accurate simulation of flow in the presence of complex boundaries one must have both an accurate boundary discretization and a uniform distribution of particles to initialize the simulation. This process of obtaining an initial uniform distribution of particles is called “particle packing”. In this paper, we compare and implement various particle packing algorithms present in the literature. We propose an improved SPH-based algorithm which produces uniform particle distributions of both the fluid and solid domains in two and three dimensions. We demonstrate the accuracy of the new algorithm by constructing some challenging geometries. The implementation of the algorithm is open source, and the manuscript is fully reproducible.

针对包含复杂边界的流动开展高精度无网格模拟时，需通过粒子精准刻画边界形态。在不可压缩/弱可压缩流动的场景下，光滑粒子流体动力学（Smoothed Particle Hydrodynamics, SPH）方法在粒子分布均匀时拥有更高的计算精度。因此，若要实现复杂边界流动的高精度时域模拟，需同时具备精准的边界离散方案与均匀的粒子初始分布。这一获取均匀粒子初始分布的过程被称为“粒子装填（particle packing）”。本文对现有文献中的各类粒子装填算法进行了对比与实现。我们提出了一种改进的基于SPH的粒子装填算法，可在二维与三维空间中实现流体域与固体域的均匀粒子分布。我们通过构建若干具有挑战性的几何构型，验证了该新算法的计算精度。本算法的实现代码已开源，且本文手稿具备完全可复现性。