Particle-based methods are a practical tool in computational fluid dynamics, and novel types of methods have been proposed. However, widely developed Lagrangian-type formulations suffer from the nonuniform distribution of particles, which is enhanced over time and result in problems in computational efficiency and parallel computations. To mitigate these problems, a mesh-constrained discrete point (MCD) method was developed for stationary boundary problems (Matsuda et al., 2022). Although the MCD method is a meshless method that uses moving least-squares approximation, the arrangement of particles (or discrete points (DPs)) is specialized so that their positions are constrained in background meshes to obtain a closely uniform distribution. This achieves a reasonable approximation for spatial derivatives with compact stencils without encountering any ill-posed condition and leads to good performance in terms of computational efficiency. In this study, a novel meshless method based on the MCD method for incompressible flows with moving boundaries is proposed. To ensure the mesh constraint of each DP in moving boundary problems, a novel updating algorithm for the DP arrangement is developed so that the position of DPs is not only rearranged but the DPs are also reassigned the role of being on the boundary or not. The proposed method achieved reasonable results in numerical experiments for well-known moving boundary problems.

翻译：基于粒子的方法是计算流体动力学中的实用工具，各类新型方法已被提出。然而，广泛发展的拉格朗日型公式存在粒子分布不均匀的问题，该问题随时间加剧并导致计算效率和并行计算方面的问题。为缓解这些问题，针对固定边界问题开发了网格约束离散点方法（Matsuda等人，2022）。尽管MCD方法是一种使用移动最小二乘近似的无网格方法，但其粒子（或称离散点）的排布经过特殊设计，使其位置受背景网格约束以获得接近均匀的分布。这通过紧凑模板实现了空间导数的合理近似，且不会遇到任何不适定条件，从而在计算效率方面表现出良好性能。本研究提出了一种基于MCD方法的移动边界不可压缩流动新型无网格方法。为确保移动边界问题中每个离散点的网格约束，开发了一种新颖的离散点排布更新算法，使得离散点不仅被重新排布，其边界/非边界的角色属性也被重新分配。在经典移动边界问题的数值实验中，所提方法取得了合理的结果。