湍流非统计平衡下的算法与模型
Algorithms and Models for Turbulence Not at Statistical Equilibrium
AI总结：
本文提出改进的涡黏模型，通过方差演化方程推导，并给出修正算法以保留真实雷诺应力特征，通过数值测试验证了间歇性反散射的实现。
摘要：
标准涡黏模型虽然稳健，但无法表示反散射且在非统计平衡复杂湍流中存在严重困难。本文通过湍流流体中方差演化方程推导了新的涡黏模型，并展示如何修正涡黏模型。证明修正模型保留了真实雷诺应力的重要特征。给出了其离散化算法，包括最小侵入式模块步骤以适应扩展模型。用通常和过扩散的Smagorinsky模型进行了数值测试。修正（缩放为10^-8）成功展示了间歇性反散射。
英文摘要：
Standard eddy viscosity models, while robust, cannot represent backscatter and have severe difficulties with complex turbulence not at statistical equilibrium. This report gives a new derivation of eddy viscosity models from an equation for the evolution of variance in a turbulent flow. The new derivation also shows how to correct eddy viscosity models. The report proves the corrected models preserve important features of the true Reynolds stresses. It gives algorithms for their discretization including a minimally invasive modular step to adapt an eddy viscosity code to the extended models. A numerical test is given with the usual and over diffusive Smagorinsky model. The correction (scaled by $10^{-8}$ ) does successfully exhibit intermittent backscatter.
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