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Analysis of the numerical dissipation rate of different Runge–Kutta and velocity interpolation methods in an unstructured collocated finite volume method in OpenFOAM®
Computer Physics Communications ( IF 6.3 ) Pub Date : 2020-08-01 , DOI: 10.1016/j.cpc.2020.107145
E.M.J. Komen , E.M.A. Frederix , T.H.J. Coppen , V. D’Alessandro , J.G.M. Kuerten

Abstract The approach used for computation of the convecting face fluxes and the cell face velocities results in different underlying numerical algorithms in finite volume collocated grid solvers for the incompressible Navier–Stokes equations. In this study, the effect of the following five numerical algorithms on the numerical dissipation rate and on the temporal consistency of a selection of Runge–Kutta schemes is analysed: (1) the original algorithm of Rhie and Chow (1983), (2) the standard OpenFOAM method, (3) the algorithm used by Vuorinen et al. (2014), (4) the Kazemi-Kamyab et al. (2015) method, and (5) the D’Alessandro et al. (2018) approach. The last three algorithms refer to recent implementations of low dissipative numerical methods in OpenFOAM®. No new computational methods are presented in this paper. Instead, the main scientific contributions of this paper are: (1) the systematic assessment of the effect of the considered five numerical approaches on the numerical dissipation rate and on the temporal consistency of the selected Runge–Kutta schemes within one unified framework which we have implemented in OpenFOAM, and (2) the application of the method of Komen et al. (2017) in order to quantify the numerical dissipation rate introduced by three of the five numerical methods in quasi-DNS and under-resolved DNS of fully-developed turbulent channel flow. In addition, we explain the effects of the introduced numerical dissipation on the observed trends in the corresponding numerical results. As one of the major conclusions, we found that the pressure error, which is introduced due to the application of a compact stencil in the pressure Poisson equation, causes a reduction of the order of accuracy of the temporal schemes for the test cases in this study. Consequently, application of higher order temporal schemes is not useful from an accuracy point of view, and the application of a second order temporal scheme appears to be sufficient.

中文翻译:

OpenFOAM® 中非结构化并置有限体积法中不同 Runge-Kutta 和速度插值方法的数值耗散率分析

摘要 用于计算对流面通量和单元面速度的方法在不可压缩 Navier-Stokes 方程的有限体积并置网格求解器中产生不同的基础数值算法。在本研究中,分析了以下五种数值算法对数值耗散率和选择的 Runge-Kutta 方案的时间一致性的影响:(1)Rhie 和 Chow(1983)的原始算法,(2)标准的 OpenFOAM 方法,(3)Vuorinen 等人使用的算法。(2014), (4) Kazemi-Kamyab 等人。(2015) 方法,以及 (5) D'Alessandro 等人。(2018) 方法。最后三种算法是指 OpenFOAM® 中低耗散数值方法的最新实现。本文没有提出新的计算方法。反而,本文的主要科学贡献是:(1)系统评估了所考虑的五种数值方法对数值耗散率和所选 Runge-Kutta 方案在一个统一框架内的时间一致性的影响。 OpenFOAM,以及(2)Komen等人方法的应用。(2017) 为了量化由五种数值方法中的三种在完全发展的湍流通道流的准 DNS 和欠解析 DNS 中引入的数值耗散率。此外,我们解释了引入的数值耗散对相应数值结果中观察到的趋势的影响。作为主要结论之一,我们发现由于在压力泊松方程中应用紧凑模板而引入的压力误差,导致本研究中测试用例的时间方案的准确性顺序降低。因此,从准确性的角度来看,高阶时间方案的应用是没有用的,而二阶时间方案的应用似乎就足够了。
更新日期:2020-08-01
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