A transport point method for complex flow problems with free surface
A transport point method for complex flow problems with free surface
复制标题
自由液面复杂流动问题的传输点法
DOI：
10.1007/s40571-019-00282-9
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发表时间：
2020-03
影响因子：
3.3
通讯作者：
Xiong Zhang
中科院分区：
文献类型：
--
作者：
Yan Song;Yan Liu;Xiong Zhang
材料点法在工程中有着广泛的应用。然而，它仍然存在准确性问题。精度问题的最重要来源之一是粒子求积的误差。形状函数梯度的不连续性会导致严重的交叉网格误差。本文提出了一种新的传输点方法（TPM），它采用了一种混合求积格式，结合了内部单元的高斯求积和边界单元的粒子求积。TPM和MPM之间的主要区别是颗粒携带的量。TPM中的输运点没有体积，只携带密集量，具有欧拉和拉格朗日的对偶性质。MLS方法用于重建单元中心和节点处的量，积分权重为单元体积。提出了一种点重排算法，在保证重构流场精度的前提下，可以任意增加、移动或删除传输点，消除数值断裂和施加入口条件。
The material point method (MPM) has been widely used in a broad area of engineering. However, it still suffers from the accuracy problem. One of the most important sources of the accuracy problem is the error of particle quadrature. The discontinuity of the gradient of the shape function causes severe crossing-mesh error. This paper proposes a new transport point method (TPM) which employs a mixed quadrature scheme combining Gaussian quadrature in the internal cells and particle quadrature in the boundary cells. The main distinction between the TPM and MPM is the quantities carried by particles. The transport points in TPM do not have volume and only carry intensive quantities and have dual properties of both Euler and Lagrange. The MLS method is used to reconstruct quantities at cell centers and nodes, and the integral weight is the cell volume. A point rearrangement algorithm is proposed so that the transport points can be added, moved or deleted arbitrarily as long as the accuracy of the reconstructed flow field is maintained, which can be used to eliminate the numerical fracture and impose inlet condition.
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