Numerical treatment of complicated wall geometry has been one of the most important challenges in particle methods for computational fluid dynamics. In this study, a novel wall boundary treatment using analytical volume integrations has been developed for two‐dimensional (2D) incompressible flow simulations with the moving particle semi‐implicit method. In our approach, wall geometry is represented by a set of line segments in 2D space. Thus, arbitrary‐shaped boundaries can easily be handled without auxiliary boundary particles. The wall's contributions to the spatial derivatives as well as the particle number density are formulated based on volume integrations over the solid domain. These volume integrations are analytically solved. Therefore, it does not entail an expensive calculation cost nor compromise accuracy. Numerical simulations have been carried out for several test cases including the plane Poiseuille flow, a hydrostatic pressure problem with complicated shape, a high viscous flow driven by a rotating screw, a free‐surface flow driven by a rotating cylinder and a dam break in a tank with a wedge. The results obtained using the proposed method agreed well with analytical solutions, experimental observations or calculation results obtained using finite volume method (FVM), which confirms that the proposed wall boundary treatment is accurate and robust.

中文翻译：

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在粒子方法中使用分析体积积分的墙边界处理

复杂壁几何结构的数值处理已成为用于计算流体动力学的粒子方法中最重要的挑战之一。在这项研究中，已经开发了一种使用分析体积积分的新型墙体边界处理方法，用于采用运动粒子半隐式方法进行的二维（2D）不可压缩流模拟。在我们的方法中，墙的几何形状由2D空间中的一组线段表示。因此，无需辅助边界粒子即可轻松处理任意形状的边界。墙对空间导数的贡献以及粒子数的密度是基于固体域上的体积积分来确定的。这些体积积分可以通过解析来解决。因此，它既不会导致昂贵的计算成本，也不会损害准确性。在几个测试案例中进行了数值模拟，包括平面泊索流，形状复杂的静水压力问题，由旋转螺杆驱动的高粘性流，由旋转圆柱体驱动的自由表面流以及坝体破裂。楔形坦克。使用所提出的方法获得的结果与解析解，实验观察结果或使用有限体积法（FVM）获得的计算结果吻合得很好，这证实了所提出的壁边界处理是准确且稳健的。