On the Influence of Polynomial De-aliasing on Subgrid Scale Models
On the Influence of Polynomial De-aliasing on Subgrid Scale Models
复制标题
多项式去锯齿对次网格尺度模型的影响
DOI：
10.1007/s10494-016-9704-y
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
C. Munz
中科院分区：
文献类型：
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作者：
A. Beck;David G. Flad;C. Tonhäuser;G. Gassner;C. Munz
在这项工作中，我们调查的多项式去混叠和亚网格尺度模型的大涡模拟的基础上不连续的Galerkin离散的相互作用。众所周知，当用高阶节点配置型离散方法模拟欠分辨湍流时，稳定性是一个主要问题。通过增加正交点的数量（多项式去混叠）将节点配置型离散化的插值特性改变为基于投影的离散化，能够消除混叠引起的稳定性问题。我们专注于这种效果和显式亚网格尺度模型的大涡模拟的后果。通常，亚网格尺度模型必须在单个模拟中实现两个可能相互冲突的任务：首先稳定数值，其次模拟缺失尺度的物理效应。在一个不连续的Galerkin方法，它可以使用一个快速的（但可能混淆折磨）节点配置离散化或基于投影的（但计算成本高）的变体结合显式的亚网格尺度模型。我们使用这个框架来调查一个标准的Smagorinsky亚网格尺度模型和变分多尺度Smagorinsky制定适当的模型参数的效果。为此，我们首先考虑的3-D粘性泰勒-格林涡的例子，调查的方法的稳定性的影响，第二个通过圆柱体的湍流流动调查和比较的结果的准确性。我们发现，混叠的不稳定性的搭配离散严重限制了模型常数的选择，特别是高阶计划，而对于去混叠DG计划，封闭模型参数可以选择独立的数值方案。对于圆柱流，我们还发现，对于相同的模型设置，基于投影的结果是在更好的协议与参考DNS比的搭配方案。
In this work we investigate the interplay of polynomial de-aliasing and sub-grid scale models for large eddy simulations based on discontinuous Galerkin discretizations. It is known that stability is a major concern when simulating underresolved turbulent flows with high order nodal collocation type discretizations. By changing the interpolatory character of the nodal collocation type discretization to a projection based discretization by increasing the number of quadrature points (polynomial de-aliasing), one is able to remove the aliasing induced stability problems. We focus on this effect and on the consequence for large eddy simulations with explicit subgrid scale models. Often, subgrid scale models have to achieve two possibly conflicting tasks in a single simulation: firstly stabilizing the numerics and secondly modeling the physical effect of the missing scales. Within a discontinuous Galerkin approach, it is possible to use either a fast (but potentially aliasing afflicted) nodal collocation discretization or a projection-based (but computationally costly) variant in combination with an explicit subgrid scale model. We use this framework to investigate the effect on the appropriate model parameter of a standard Smagorinsky subgrid scale model and of a Variational Multiscale Smagorinsky formulation. For this we first consider the 3-D viscous Taylor-Green vortex example to investigate the impact on the stability of the method and second the turbulent flow past a circular cylinder to investigate and compare the accuracy of the results. We show that the aliasing instabilities of collocative discretizations severely limit the choice of the model constant, in particular for high order schemes, while for de-aliased DG schemes, the closure model parameters can be chosen independently from the numerical scheme. For the cylinder flow, we also find that for the same model settings, the projection-based results are in better agreement with the reference DNS than those of the collocative scheme.