论文标题
基于能量的长度尺寸，用于减少湍流的顺序模型
An Energy-Based Lengthscale for Reduced Order Models of Turbulent Flows
论文作者
论文摘要
在本文中，我们提出了一种新颖的减少顺序模型（ROM）长度尺度，该模型是通过使用能量分布参数构建的。新的基于能量的ROM长度尺度与当前的ROM长度尺度有根本不同，后者是通过使用维参数构建的。为了评估新颖的基于能量的ROM长度尺度，我们将其与标准的，基于维度的ROM长度尺寸进行比较，其中两种基本不同类型的模型：（i）混合长度ROM（ML-ROM），这是ROM闭合模型； （ii）Evolve-Filter-Relax ROM（EFR-ROM），它是正规化的ROM。我们在湍流通道流量的数值模拟中测试了四个组合（即配备了基于能量和基于尺寸的长度尺度的ML-ROM和EFR-ROM）。数值调查得出以下结论：（i）基于能量的ROM长度尺度明显（几乎两个数量级）大于基于标准维度的ROM长度尺度。结果，基于能量的长度尺寸比基于维度的长度尺寸产生的ML-ROM和EFR-ROM更稳定。 （ii）基于能量的长度尺寸显示了相对于ROM维度正确的渐近行为，而基于维度的长度却没有。 （iii）基于能量的长度尺寸产生ML-ROM，并且（当显着过滤时）EFR-ROM的参数比基于基于维度的长度尺寸的ML-ROM和EFR-ROM的参数敏感（即更健壮）的敏感性（即更健壮）。新型的基于能量的长度尺寸可以使得针对特定于流的应用的更好的规模感知ROM策略的发展，并有望在核反应堆热液压液中长期应用。
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.
