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：[翻译摘要] 粒子方法作为计算流体动力学的实用工具，已有多种新型方法被提出。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，该问题会随时间加剧，导致计算效率和并行计算方面出现困难。为解决这些问题，研究人员针对固定边界问题开发了网格约束离散点法（MCD法，Matsuda等，2022）。该无网格方法采用移动最小二乘近似，但其粒子（即离散点）的排布经过特殊设计，使其位置受背景网格约束，从而获得近乎均匀的分布。这确保了在使用紧致模板进行空间导数近似时既能获得合理精度又不会产生病态条件，进而展现出良好的计算效率。本研究在MCD法基础上，提出了一种适用于含移动边界不可压缩流的新型无网格方法。为确保移动边界问题中每个离散点满足网格约束，我们开发了全新的离散点排布更新算法：该算法不仅重新排布离散点位置，还重新分配其是否作为边界点的角色。数值实验表明，该方法在经典移动边界问题中取得了合理的结果。