Boundary integral based polygon wall representation in the MPS method
Boundary integral based polygon wall representation in the MPS method
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DOI：
10.1299/transjsme.18-00197
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
T. Matsunaga;K. Shibata;S. Koshizuka
中科院分区：
文献类型：
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作者：
T. Matsunaga;K. Shibata;S. Koshizuka
粒子方法适合于模拟边界大变形的流体粘性流动问题。移动粒子半隐式（MPS）方法是求解不可压湍流问题的典型粒子方法之一。近年来，MPS方法在科学和工程的各个领域受到了极大的关注。然而，复杂壁面几何形状的数值处理仍然是一个悬而未决的问题。传统的方法在处理任意形状或计算精度方面存在严重问题。在这种情况下，本研究提出了一种新的MPS方法中的固体壁边界的数值处理。在这种方法中，离散格式中的壁贡献以物体域上的体积积分的形式来描述。因此，可以忠实地考虑由多边形网格表示的任意形状的边界。此外，由于物体内部的物理量分布是通过线性外推给出的，因此它以高精度满足规定的边界条件。虽然体积积分不能以可承受的计算成本进行数值计算，但它可以基于发散定理转化为边界积分形式。导出的边界积分可以计算合理的成本和可接受的精度使用投影技术和高斯求积。所提出的方法已通过几个数值测试的情况下，在2D和3D。数值试验结果表明，与传统方法相比，本文方法具有较高的精度，其有效性得到了艾德的验证.壁粒子表示。另一方面，传统的壁权函数大大低估了壁的贡献在一个凹的角落。
The particle methods are suited to simulate fluid flow problems with large boundary deformation. The moving particle semi-implicit (MPS) method is one of the representative particle methods for incompressible flow. In recent years, the MPS method has received a great deal of attention in various fields of science and engineering. However, the numerical treatment of complicated wall geometry is still an open question. The conventional approaches have severe issues in handling arbitrary shape or calculation accuracy. In these circumstances, this study has been done to propose a novel numerical treatment of solid wall boundary in the MPS method. In this approach, the wall contribution in the discretization scheme is described in a form of volume integral over object domain. Thus, arbitrary-shaped boundaries represented by a polygon mesh can faithfully be considered. Moreover, since the distribution of physical quantity inside object is given by linear extrapolation, it satisfies the prescribed boundary condition with high accuracy. While the volume integral cannot be numerically evaluated with affordable computational cost, it can be transformed into a boundary integral form based on the divergence theorem. The derived boundary integral can be calculated with reasonable cost and acceptable accuracy using a projection technique and the Gaussian quadrature. The proposed method has been examined through several numerical test cases in 2D and 3D. As a result of the numerical tests, the present method is shown to have considerably higher accuracy compared to conventional methods, and its validity is verified. the wall particle representation. On the other hand, the conventional wall weight function considerably underestimates the wall contribution at a concave corner.