Elimination of Artificial Grid Distortion and Hourglass-Type Motions by Means of Lagrangian Subzonal Masses and Pressures
Elimination of Artificial Grid Distortion and Hourglass-Type Motions by Means of Lagrangian Subzonal Masses and Pressures
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DOI：
10.1006/jcph.1998.5952
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发表时间：
1998-05
影响因子：
4.1
通讯作者：
E. Caramana;M. Shashkov
中科院分区：
文献类型：
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作者：
E. Caramana;M. Shashkov
拉格朗日流体动力学计算的祸根是网格拓扑结构的过早崩溃，导致精度严重下降和运行终止，通常远在拉格朗日带状质量的假设不再有效之前。在短的空间网格尺度上，这通常被称为“沙漏”模式或“梯形”运动，特别是与欠约束网格相关，如二维和三维的四边形和六面体。在相对于网格间距较长的空间长度上，存在普遍称为“假涡度”或细长带问题。在这两种情况下，结果都是与实际解无关的异常网格畸变和缠结，就像湍流的情况一样。在这项工作中，我们将展示如何消除这种运动可以通过适当使用亚带拉格朗日质量，以及相关的密度和压力。这些次带压力产生抵抗这些虚假运动的力。压力不再是一个恒定的区域;它现在准确地反映了密度梯度，可能会出现在一个区域内，由于其差分失真。亚带拉格朗日质量可以以多种方式选择，以获得亚带密度和压力变化。然而，这些群众出现在一个自然的方式从拉格朗日轮廓的交叉点，通过没有质量流，这是与拉格朗日带状和节点群众在交错的空间网格流体动力学配方。这是通常拉格朗日假设的延伸，通常只适用于带状质量。我们表明，与适当的离散化的副带压力，沙漏运动和虚假涡产生的副带力可以消除一个非常大的问题。
The bane of Lagrangian hydrodynamics calculations is the premature breakdown of grid topology that results in severe degradation of accuracy and run termination often long before the assumption of a Lagrangian zonal mass has ceased to be valid. At short spatial grid scales this is usually referred to by the terms “hourglass” mode or “keystone” motion associated, in particular, with underconstrained grids such as quadrilaterals and hexahedrons in two and three dimensions, respectively. At longer spatial lengths relative to the grid spacing there is what is referred to ubiquitously as “spurious vorticity,” or the long-thin zone problem. In both cases the result is anomalous grid distortion and tangling that has nothing to do with the actual solution, as would be the case for turbulent flow. In this work we show how such motions can be eliminated by the proper use of subzonal Lagrangian masses, and associated densities and pressures. These subzonal pressures give rise to forces that resist these spurious motions. The pressure is no longer a constant in a zone; it now accurately reflects the density gradients that can occur within a zone due to its differential distortion. Subzonal Lagrangian masses can be choosen in more than one manner to obtain subzonal density and pressure variation. However, these masses arise in a natural way from the intersection of the Lagrangian contours, through which no mass flows, that are associated with both the Lagrangian zonal and nodal masses in a staggered spatial grid hydrodynamics formulation. This is an extension of the usual Lagrangian assumption that is often applied to only the zonal mass. We show that with a proper discretization of the subzonal forces resulting from subzonal pressures, hourglass motion and spurious vorticity can be eliminated for a very large range of problems.