A Lagrangian nodal integration method for free-surface fluid flows
A Lagrangian nodal integration method for free-surface fluid flows
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DOI：
10.1016/j.cma.2019.112816
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发表时间：
2020-04-01
影响因子：
7.2
通讯作者：
Onate, Eugenio
中科院分区：
文献类型：
--
作者：
Franci, Alessandro;Cremonesi, Massimiliano;Onate, Eugenio
本文提出了一种模拟牛顿和非牛顿自由表面流体流动的拉格朗日节点积分法。所提出的节点拉格朗日方法使用有限元网格来离散计算域，并定义未知节点变量的（线性）形状函数，如在标准的粒子有限元法（PFEM）。然而，在这种方法中，积分是在节点片上而不是在单元上进行的，应变/应力是在节点上而不是在高斯点上定义的。这允许限制与重新划分网格相关联的缺点，并导致比经典的单元PFEM更精确的应力计算。几个数值试验，在2D和3D，提出了验证所提出的节点PFEM。在所有情况下，该方法已显示出很好的协议与解析解和实验和数值结果从文献。节点和元素PFEM之间进行了彻底的比较，专注于关键问题，如解决方案的精度，收敛性，质量守恒和网格变形的敏感性。(C)2019年爱思唯尔B.Y. All rights reserved.
We present a Lagrangian nodal integration method for the simulation of Newtonian and non-Newtonian free-surface fluid flows. The proposed nodal Lagrangian method uses a finite element mesh to discretize the computational domain and to define the (linear) shape functions for the unknown nodal variables, as in the standard Particle Finite Element Method (PFEM). In this approach, however, the integrals are performed over nodal patches and not over elements, and strains/stresses are defined at nodes and not at Gauss points. This allows to limit the drawbacks associated with the remeshing and leads to a more accurate stress computation than in the classical elemental PFEM. Several numerical tests, in 2D and in 3D, are presented to validate the proposed nodal PFEM. In all cases, the method has shown a very good agreement with analytical solutions and with experimental and numerical results from the literature. A thorough comparison between nodal and elemental PFEMs is also presented, focusing on crucial issues, such as solution accuracy, convergence, mass conservation and sensitivity to mesh distortion. (C) 2019 Elsevier B.Y. All rights reserved.