Elimination of hourglass distortions by means of the Lagrangian–Gauss-point-mass method for compressible fluid flows
Elimination of hourglass distortions by means of the Lagrangian–Gauss-point-mass method for compressible fluid flows
复制标题
通过可压缩流体流动的拉格朗日高斯点质量法消除沙漏变形
DOI：
10.1016/j.compfluid.2015.04.013
复制
发表时间：
2015-08
期刊：
影响因子：
--
通讯作者：
Baolin Tian
中科院分区：
文献类型：
--
作者：
Junxia Cheng;Baolin Tian
具有恒定应力的四边形或六面体上的交错拉格朗日格式多年来一直受到沙漏扭曲的困扰。沙漏粘性常被用来抑制沙漏扭曲导致的非保守总能量，尽管如此，计算经常因为虚假的大网格扭曲而异常停止。在多维问题中，很难区分物理失真和虚假失真，因此我们希望得到消除沙漏失真的方案。本文利用拉格朗日高斯点质量(LGM)方法给出了一种新的可压缩流动的拉格朗日格式以消除网格沙漏运动。在LGM方法中，与亚纬向压力方法相似，压力在一个区域内变化，但它们之间有几个重要的区别。数值算例表明，LGM方法可以消除许多问题的沙漏运动，并具有在二维平面几何中几乎保持总能量守恒的良好性质。由于面积加权方案不能保持总能量，但在很大程度上改善了总能量。LGM方法在已有的四边形上的二维有限元程序中实现简单，并可推广到六面体上的三维有限元程序中，理论上没有困难。
Staggered Lagrangian schemes on quadrilaterals or hexahedrons with constant stress have been troubled by hourglass distortions for many years. Hourglass viscosities have been often used to suppress hourglass distortions resulting in the nonconservative total energy, even so computations often halt abnormally because of spurious large grid distortions. It is difficult to discern the spurious distortions from the physical in multidimensional problems, so we want to get the scheme eliminating hourglass distortions. This paper gives a new Lagrangian scheme for compressible flows to eliminates the grid hourglass motions by means of the Lagrangian Gauss-point Mass (LGM) method. In the LGM method, pressures are varied in a zone similar to the subzonal pressure method, but there are several important differences between them. Numerical examples show that the LGM method can eliminate the hourglass motions for many problems, and it has the good property of preserving the conservation of total energy nearly in the two-dimensional plane geometry. Because of the area-weighted scheme, it cannot preserve the total energy but improves it to a great extent. The procedure of the LGM method is simple to be implemented into the existing 2D finite element codes on quadrilaterals, and it can be extended to the 3D finite element codes on hexahedrons without theoretical difficulties.
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DOI：
--
发表时间：
1955-01
期刊：
--
影响因子：
--
作者：
R. Landshoff
通讯作者：
R. Landshoff
影响因子：
4.1
作者：
J. Dukowicz;B. Meltz
通讯作者：
J. Dukowicz;B. Meltz
影响因子：
4.1
作者：
E. Caramana;M. Shashkov
通讯作者：
E. Caramana;M. Shashkov
影响因子：
3.2
作者：
VONNEUMANN, J;RICHTMYER, RD
通讯作者：
RICHTMYER, RD
影响因子：
4.1
作者：
W. F. Noh
通讯作者：
W. F. Noh