Analysis of interpolation schemes for the accurate estimation of energy spectrum in Lagrangian methods
Analysis of interpolation schemes for the accurate estimation of energy spectrum in Lagrangian methods
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DOI：
10.1016/j.compfluid.2013.05.003
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发表时间：
2013-08-15
影响因子：
2.8
通讯作者：
Adams, Nikolaus A.
中科院分区：
文献类型：
--
作者：
Shi, Yilei;Zhu, Xiao Xiang;Adams, Nikolaus A.
直接计算纯拉格朗日无网格法的能谱是一项具有挑战性的任务。另一方面，在拉格朗日框架下湍流模型的改进很大程度上依赖于我们估计最大分辨波数的能谱的能力。在本文中，我们比较了不同的策略，从定义在一组散乱的点上的速度场中提取能量谱。利用离散傅里叶变换(DFT)及其正则化形式，可以直接从不规则分布的样本中估计光谱。替代程序需要对网格进行初步内插，在第二阶段，可以执行傅里叶分析。作为最后一种方法，研究了一种用于初始内插的移动最小二乘(MLSS)技术，并对结果进行了讨论。尽管在中低波数窗口表现出良好的精度，但前两种策略在接近最大分辨率的波数中引入了不可接受的大误差，其中通常需要最高的精度。在这里，我们提出了一个二阶移动最小二乘(MLSS)方案作为一种优化工具，使我们能够精确地重现整个波数窗口的能谱。我们讨论了这一结果对于发展精确的纯拉格朗日无网格法湍流模型的重要性。(C)2013爱思唯尔有限公司。保留所有权利。
Direct evaluation of energy spectra in purely Lagrangian meshless methods is a challenging task. On the other hand, improvement of turbulence modeling in a Lagrangian framework relies strongly on our ability to estimate energy spectra up to the maximally resolved wavenumber. In this paper we compare different strategies to extract energy spectra from a velocity field defined on a scattered set of points. Spectra can be directly evaluated from irregularly distributed sample by using Discrete Fourier Transform (DFT) and their regularized versions. Alternative procedures require a preliminary interpolation into a grid where, on a second stage, a Fourier analysis can be performed. As a last approach a Moving Least Squares (MLSs) technique for preliminary interpolation is investigated and the results are discussed. Although exhibiting good accuracy in the low-moderate wavenumber window, the first two strategies introduce unacceptable large errors in the near-maximal-resolved wavenumber, where the highest accuracy is often required. Here we propose a second-order Moving Least Squares (MLSs) scheme as an optimal tool that allows us to reproduce precisely the energy spectrum over the entire wavenumber window. We discuss the importance of this result with respect to the development of accurate turbulence models for purely Lagrangian meshless methods. (C) 2013 Elsevier Ltd. All rights reserved.