湍流降阶模型的能量尺度
An Energy-Based Lengthscale for Reduced Order Models of Turbulent Flows
摘要：
在本文中，我们提出了一种新的降阶模型（ROM）的长度尺度，构造通过使用能量分布参数。新的基于能量的ROM长度尺度从根本上不同于当前的ROM长度尺度，当前的ROM长度尺度是通过使用维度参数构建的。为了评估新的基于能量的ROM长度尺度，我们将其与标准的基于维度的ROM长度尺度在两种根本不同类型的模型中进行比较：（i）混合长度ROM（ML-ROM），其是ROM闭合模型;以及（ii）进化过滤器放松ROM（EFR-ROM），其是正则化ROM。ML-ROM和EFR-ROM（配备了基于能量和基于量纲的长度尺度）在$Re_τ = 395$湍流槽道流动数值模拟中的应用。数值研究得出以下结论：（i）新的基于能量的ROM长度尺度明显（几乎两个数量级）大于标准的基于维数的ROM长度尺度。结果，基于能量的长度尺度比基于维度的长度尺度产生更稳定的ML-ROM和EFR-ROM。(ii)基于能量的长度尺度相对于ROM维度显示正确的渐近行为，而基于维度的长度尺度不显示。(iii)基于能量的长度尺度产生ML-ROM和（当实现显著滤波时）参数较不敏感的EFR-ROM（即，更鲁棒）。新的能量为基础的长度尺度可以使更好的规模感知ROM策略的发展流动特定的应用，预计将在核反应堆热工水力学的长期应用。
英文摘要：
In this paper, we propose a novel reduced order model (ROM) lengthscale that is constructed by using energy distribution arguments. The new energy-based ROM lengthscale is fundamentally different from the current ROM lengthscales, which are built by using dimensional arguments. To assess the novel, energy-based ROM lengthscale, we compare it with a standard, dimensionality-based ROM lengthscale in two fundamentally different types of models: (i) the mixing-length ROM (ML-ROM), which is a ROM closure model; and (ii) the evolve-filter-relax ROM (EFR-ROM), which is a regularized ROM. We test the four combinations (i.e., ML-ROM and EFR-ROM equipped with the energy-based and dimensionality-based lengthscales) in the numerical simulation of the turbulent channel flow at $Re_τ = 395$. The numerical investigation yields the following conclusions: (i) The new energy-based ROM lengthscale is significantly (almost two orders of magnitude) larger than the standard dimensionality-based ROM lengthscale. As a result, the energy-based lengthscale yields more stable ML-ROMs and EFR-ROMs than the dimensionality-based lengthscale. (ii) The energy-based lengthscale displays the correct asymptotic behavior with respect to the ROM dimension, whereas the dimensionality-based lengthscale does not. (iii) The energy-based lengthscale yields ML-ROMs and (when significant filtering is effected) EFR-ROMs whose parameters are less sensitive (i.e., more robust) than the parameters of the ML-ROMs and EFR-ROMs based on the dimensionality-based lengthscale. The novel energy-based lengthscale could enable the development of better scale-aware ROM strategies for flow-specific applications and is expected to have long term applications in nuclear reactor thermal-hydraulics.
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