一种改进的Smagorinsky亚格子模型用于湍流大涡模拟
A Modified Smagorinsky Subgrid Scale Model for the Large Eddy Simulation of Turbulent Flow
AI总结：
本文提出一种改进的Smagorinsky亚格子模型，以修正近壁面性能并最小化计算开销，并在有限元框架下分析滤波与微分互换误差。
摘要：
在大涡模拟领域，Smagorinsky亚格子模型（以某种形式）是最被普遍接受和使用的亚格子模型。本文旨在解决Smagorinsky模型的主要弱点，即其在近壁面附近的性能不佳。目标是建立一个能在近壁面修正Smagorinsky模型，同时最小化计算开销的模型。动态亚格子模型的一个版本也被纳入有限元代码中，以便在近壁面附近与新模型进行比较。\n 与其他处理湍流的方法相比，大涡模拟的一个独特特征是滤波的思想。在本文中，我们定义了什么是滤波器，并解决了与滤波器相关的一个问题：当滤波运算和微分运算互换时所产生的误差。该误差在有限元方法的背景下进行研究，这使我们能够专注于被滤波的函数而不是滤波核函数，而后者是研究该误差时通常采用的方法。
英文摘要：
In the field of Large Eddy Simulation, the Smagorinsky subgrid scale model (in some form) is the most commonly accepted and used subgrid scale model. The purpose of this paper is to address the main weakness of the Smagorinsky model, its poor performance near the wall. The goal is to establish a model that corrects the Smagorinsky model near the walls while at the same time minimizing the computational overhead. A version the Dynamic Subgrid Scale model is also incorporated into the finite element code to facilitate comparisons with the new model near the walls. One of the unique characteristics of Large Eddy Simulations as compared to other methods of dealing with turbulent flows is the idea of filtering. In this paper we define what a filter is and also address an issue related to filters; the error that results when the filtering and differential operations are interchanged. This error is studied under the context of the Finite Element Method which allows us to focus on the function being filtered rather than the filter kernal function, which has been the usual approach in studying this error.
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