A Spectrally Reduced Dynamic Turbulence Subgrid Model

光谱简化的动态湍流子网格模型

• 批准号: 203226-2007
• 负责人: Bowman, John
• 金额: $ 1.46万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2009
• 资助国家: 加拿大
• 起止时间: 2009-01-01 至 2010-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=423898
• 关键词: Spectrally; Reduced; Dynamic; Turbulence; Subgrid

The understanding of fully developed turbulence remains an elusive challenge to researchers in science and engineering. Although the Navier-Stokes equation provides an accurate description of typical fluids, when it becomes chaotic at high speeds, our understanding is rudimentary. Indeed, substantial progress towards understanding this equation and its solutions constitutes one of the seven millennium challenges proposed by the Clay Mathematics Institute. Even approximate solutions of the problem defy modern computers, which lack the storage and speed necessary to accurately simulate turbulence in the Earth's atmosphere or around a moving body. Subgrid models are often used to allow a simulation on today's computer to mimic computations that will very likely not be directly possible even on the computers of the next century. However, most of the subgrid models used in practice are ad hoc devices that remove energy from the system at the smallest scales retained in the simulation. However, for a subgrid model to be faithful to the underlying physics, it must also inject energy at other scales, to describe the beating of small-scale waves. This important effect is neglected by many subgrid models in use today. The goal of this project is to develop reliable subgrid models for the next generation of turbulence simulations, based on a technique known as spectral reduction, which allows one to accurately estimate velocities at scales that are not directly retained in the simulation. Recently, a practical computational technique for applying spectral reduction to a one-dimensional analogue of the Navier-Stokes equation (with which it shares many properties) was developed in a master's thesis. The method is an attempt to numerically approximate the solution using several grids of variable resolution. The communication of data between the grids is designed to conserve energy. The generalization of the method to the full Navier-Stokes equation would lead to a dynamical subgrid model for high-Reynolds number turbulence that has a physical basis and is free of arbitrary parametrization. Such a subgrid model would greatly reduce the computational cost of simulations of turbulent drag and transport.

对于科学和工程研究人员来说，理解完全发展的湍流仍然是一个难以捉摸的挑战。 尽管纳维-斯托克斯方程提供了对典型流体的准确描述，但当它在高速下变得混乱时，我们的理解还很初级。事实上，在理解这个方程及其解决方案方面取得的实质性进展构成了克莱数学研究所提出的七个千年挑战之一。 即使是这个问题的近似解决方案也无法解决现代计算机的问题，因为现代计算机缺乏精确模拟地球大气层或运动物体周围湍流所需的存储空间和速度。 子网格模型通常用于允许在当今的计算机上进行模拟，以模仿即使在下个世纪的计算机上也很可能无法直接实现的计算。然而，实践中使用的大多数子网格模型都是临时设备，它们以模拟中保留的最小规模从系统中移除能量。 然而，为了使子网格模型忠实于基础物理，它还必须注入其他尺度的能量，以描述小尺度波的跳动。 当今使用的许多子网格模型都忽略了这一重要影响。 该项目的目标是基于一种称为谱缩减的技术，为下一代湍流模拟开发可靠的子网格模型，该技术允许人们准确估计模拟中不直接保留的尺度上的速度。 最近，一篇硕士论文开发了一种实用的计算技术，用于将谱缩减应用于纳维-斯托克斯方程的一维模拟（与其共享许多属性）。 该方法尝试使用多个可变分辨率网格来数值近似解。网格之间的数据通信旨在节约能源。 该方法推广到完整的纳维-斯托克斯方程将产生高雷诺数湍流的动态子网格模型，该模型具有物理基础并且不受任意参数化的影响。这样的子网格模型将大大降低湍流阻力和传输模拟的计算成本。