High‐order discontinuous Galerkin spectral element methods for transitional and turbulent flow simulations
High‐order discontinuous Galerkin spectral element methods for transitional and turbulent flow simulations
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DOI：
10.1002/fld.3943
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发表时间：
2014-11
影响因子：
1.8
通讯作者：
A. Beck;T. Bolemann;David G. Flad;Hannes Frank;G. Gassner;F. Hindenlang;C. Munz
中科院分区：
文献类型：
--
作者：
A. Beck;T. Bolemann;David G. Flad;Hannes Frank;G. Gassner;F. Hindenlang;C. Munz
本文研究了中等雷诺数下欠分辨转捩和湍流流动的间断Galerkin谱方法模拟的准确性和效率，其中紧密耦合层流区域、转捩和发展湍流的准确预测对大涡模拟建模提出了巨大挑战。我们充分利用高阶谱方法的低数值误差和相关的上级尺度分辨能力，使用高达12阶的高阶反函数。我们采用多项式去混叠技术来防止非线性的不精确求积引起的不稳定性。不需要任何额外的滤波、显式或隐式建模或人工耗散，我们的高阶格式可以很好地捕捉所考虑雷诺数范围内的湍流。考虑了三个经典的大涡模拟基准问题：ReD=3900的圆柱流、Reh=2800的受限周期性山丘流和Rec= 60，000的SD7003翼型的过渡流。对于所有的计算，用于不连续Galerkin谱方法模拟的自由度的总数被选择为等于或大大小于文献中报道的数据。在所有这三种情况下，我们实现了一个相等或更好的匹配直接数值模拟结果相比，其他计划的低阶显式或隐式添加亚网格尺度模型。版权所有© 2014约翰威利父子有限公司.
In this paper, we investigate the accuracy and efficiency of discontinuous Galerkin spectral method simulations of under‐resolved transitional and turbulent flows at moderate Reynolds numbers, where the accurate prediction of closely coupled laminar regions, transition and developed turbulence presents a great challenge to large eddy simulation modelling. We take full advantage of the low numerical errors and associated superior scale resolving capabilities of high‐order spectral methods by using high‐order ansatz functions up to 12th order. We employ polynomial de‐aliasing techniques to prevent instabilities arising from inexact quadrature of nonlinearities. Without the need for any additional filtering, explicit or implicit modelling, or artificial dissipation, our high‐order schemes capture the turbulent flow at the considered Reynolds number range very well. Three classical large eddy simulation benchmark problems are considered: a circular cylinder flow at ReD=3900, a confined periodic hill flow at Reh=2800 and the transitional flow over a SD7003 airfoil at Rec=60,000. For all computations, the total number of degrees of freedom used for the discontinuous Galerkin spectral method simulations is chosen to be equal or considerably less than the reported data in literature. In all three cases, we achieve an equal or better match to direct numerical simulation results, compared with other schemes of lower order with explicitly or implicitly added subgrid scale models. Copyright © 2014 John Wiley & Sons, Ltd.