文章中的网格独立性验证

[史浩]

之前写了一篇文章，主要内容是模拟了电磁场下液滴的下落过程。其中多相流部分是采用interFoam中的算法计算的，电磁场是自己植入进去的。为了增加计算精度，采用了自适应网格细化（adaptive mesh refinement）来捕捉两相界面。
最近审稿意见回来了，里面很重要的一条是：Is the solution grid independend? Please give a proof!
自己的想法是：做不同尺寸网格下的计算，然后对比结果，结果一致就说明算法的网格独立性很好。但是感觉当网格粗大的时候VOF模型算的确实差别比较大
由于一直在用CFD做一些应用，对于网格独立性验证这东西不是很懂。这类意见大概怎么回复比较好？有没有有经验的大佬分享一下经验？

[李东岳]

你的思路是对的，

另一方面，你做的网格自适应，还可以强调网格自适应本身已经比没有自适应的降低网格相关性了。

不过既然大爷让你证明了，你只能给他算算看

[random_ran]

If you will the whole paper itself would be served as a validation
purpose.

@article{MALIZIA2019103988,
title = "CFD simulations of spoked wheel aerodynamics in cycling: Impact of computational parameters",
journal = "Journal of Wind Engineering and Industrial Aerodynamics",
volume = "194",
pages = "103988",
year = "2019",
issn = "0167-6105",
doi = "https://doi.org/10.1016/j.jweia.2019.103988",
url = "http://www.sciencedirect.com/science/article/pii/S0167610519305884",
author = "F. Malizia and H. Montazeri and B. Blocken",
keywords = "Cycling aerodynamics, Cycling spoked wheel, CFD analysis, Computational grid, Rotation modeling, Turbulence modeling",
abstract = "Spoked wheels are commonly used in cycling races and their aerodynamic performance is a critical factor in the overall cycling performance, as the wheels can be responsible for about 10% of the total cyclist-bicycle drag. Although several computational fluid dynamics (CFD) simulations have been carried out for wheel aerodynamics in the past decades, it is still not clear to which extent the outcome of such simulations is sensitive to the computational parameters set by the user. The present paper aims at defining a framework for CFD simulations of an isolated spoked wheel by a systematic sensitivity analysis focused on the computational grid, wheel rotation modeling and turbulence modeling. The results show: (i) a high sensitivity to the wheel surface grid, y+ (<4) and far-field growth rate (≤1.15); (ii) the wheel rotational approaches with moving reference frame (MRF) and hybrid MRF-RW (RW ​= ​rotating wall approach) can provide a satisfactory agreement with wind tunnel data available in the literature (+9.7% and −2.1% deviations, respectively); (iii) k-ω SST, γ-SST or realizable k-ε are suitable as turbulence models. This work is intended to stimulate the accurate and reliable application of CFD for the assessment and optimization of wheel aerodynamics."
}

[史浩]

文章被接收啦，其中的网格独立性验证各位大佬帮助很多，一并谢过 @random_ran @东岳

[李东岳]

@史浩 恭喜恭喜！！！！！！

[史浩]

@李东岳 李老师，好久不见！最近重温你写的interFoam求解器的解析，里面有一句话

VOF作为网格依赖类求解器，加密网格研究网格无关性至关重要

这里所说的网格依赖具体的标准是什么？因为所有的数值模拟结果都和网格相关，但不是所有的求解器都叫网格依赖类求解器。所以我觉得应该要满足一定的标准才能叫网格依赖类求解器，那么有没有什么文献定义过赭红标准？还只是大家经验之谈，只是觉得VOF模型受网格影响大一些？

[李东岳]

@史浩 VOF和LES都是高度网格依赖类求解器。主要是LES只能捕获大于网格尺度的涡，因此，网格越小，LES越能捕获到更小的涡。类似的，VOF捕获到的界面只能大于网格尺度，如果计算域存在气泡，如果网格越小，VOF可以捕获到的气泡越小。