On the numerical accuracy in finite-volume methods to accurately capture turbulence in compressible flows,International Journal for Numerical Methods in Fluids

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On the numerical accuracy in finite-volume methods to accurately capture turbulence in compressible flows
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2021-06-07 , DOI: 10.1002/fld.5021
Emmanuel Motheau ₁ , John Wakefield ₂

Affiliation

The goal of the present article is to understand the impact of numerical schemes for the reconstruction of data at cell faces in finite-volume methods, and to assess their interaction with the quadrature rule used to compute the average over the cell volume. Here, third-, fifth- and seventh-order WENO-Z schemes are investigated. On a problem with a smooth solution, the theoretical order of convergence rate for each method is retrieved, and changing the order of the reconstruction at cell faces does not impact the results, whereas for a shock-driven problem all the methods collapse to first-order. Study of the decay of compressible homogeneous isotropic turbulence reveals that using a high-order quadrature rule to compute the average over a finite-volume cell does not improve the spectral accuracy and that all methods present a second-order convergence rate. However the choice of the numerical method to reconstruct data at cell faces is found to be critical to correctly capture turbulent spectra. In the context of simulations with finite-volume methods of practical flows encountered in engineering applications, it becomes apparent that an efficient strategy is to perform the average integration with a low-order quadrature rule on a fine mesh resolution, whereas high-order schemes should be used to reconstruct data at cell faces.

中文翻译：

在有限体积方法中精确捕获可压缩流中的湍流的数值精度

本文的目标是了解数值方案对有限体积方法中单元面数据重建的影响，并评估它们与用于计算单元体积平均值的正交规则的相互作用。在这里，研究了三阶、五阶和七阶 WENO-Z 方案。对于平滑解的问题，检索每种方法的收敛速度的理论顺序，改变细胞面重建顺序不会影响结果，而对于冲击驱动的问题，所有方法都崩溃到第一个 -命令。对可压缩均匀各向同性湍流衰减的研究表明，使用高阶正交规则计算有限体积单元上的平均值不会提高谱精度，并且所有方法都呈现二阶收敛速度。然而，我们发现选择在单元面重建数据的数值方法对于正确捕获湍流光谱至关重要。在工程应用中遇到的实际流动的有限体积方法模拟的背景下，一个有效的策略是在精细网格分辨率上使用低阶正交规则执行平均积分，而高阶方案应该用于重建细胞面的数据。然而，我们发现选择在单元面重建数据的数值方法对于正确捕获湍流光谱至关重要。在工程应用中遇到的实际流动的有限体积方法模拟的背景下，一个有效的策略是在精细网格分辨率上使用低阶正交规则执行平均积分，而高阶方案应该用于重建细胞面的数据。然而，我们发现选择在单元面重建数据的数值方法对于正确捕获湍流光谱至关重要。在工程应用中遇到的实际流动的有限体积方法模拟的背景下，一个有效的策略是在精细网格分辨率上使用低阶正交规则执行平均积分，而高阶方案应该用于重建细胞面的数据。

更新日期：2021-06-07

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