A wall boundary treatment using analytical volume integrations in a particle method
A wall boundary treatment using analytical volume integrations in a particle method
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DOI：
10.1002/nme.6429
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发表时间：
2020-07
影响因子：
2.9
通讯作者：
T. Matsunaga;Nobuhiro Yuhashi;K. Shibata;S. Koshizuka
中科院分区：
文献类型：
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作者：
T. Matsunaga;Nobuhiro Yuhashi;K. Shibata;S. Koshizuka
复杂壁面几何的数值处理一直是计算流体力学粒子方法中最重要的挑战之一。在这项研究中，一种新的壁面边界处理使用解析体积积分已开发的二维（2D）不可压缩流模拟与移动粒子半隐式方法。在我们的方法中，墙壁的几何形状表示的一组线段在二维空间。因此，任意形状的边界可以很容易地处理，而无需辅助边界粒子。壁的贡献的空间导数以及粒子数密度的基础上制定的固体域的体积积分。这些体积积分解析求解。因此，它不需要昂贵的计算成本，也不损害精度。对几种测试情况进行了数值模拟，包括平面Poiffille流，具有复杂形状的静水压力问题，由旋转螺旋驱动的高粘性流，由旋转圆柱驱动的自由表面流和具有楔形物的储罐中的溃坝。计算结果与解析解、实验观测值和有限体积法（FVM）计算结果吻合较好，验证了所提出的壁面边界处理方法的准确性和鲁棒性。
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.