Physics-inspired Coarsening for Turbulent Flow Simulations

流体湍流是一种关键的物理现象，在广泛的工程和科学领域具有重要的意义。然而，湍流的模拟和预测是非常昂贵的，因为它们本质上是非线性的，混沌的行为涉及大范围的耦合长度和时间尺度。一种越来越有吸引力的方法是只计算大尺度运动的动力学，用模型来表示未解决特征的净效应，这种方法被称为大涡模拟（LES）。然而，基于空间滤波的LES的基本理论有几个缺点，包括缺乏对非均匀网格分辨率、边界和界面的准确、一致的处理。本提案引入了物理启发的粗化概念，作为解决这些挑战的潜在变革概念。该项目的主要目标是开发湍流模拟的物理启发框架，并在与许多感兴趣的湍流共享基本特征的代表性流动中进行测试。因此，拟议的工作旨在开发与应用相关的改变游戏规则的模拟技术，包括海洋学，大气科学，可再生能源，航空航天，推进，天体物理学，甚至人类健康。该项目将包括开发一门新的数值方法本科课程和一个完全整合的本科研究项目，作为加州大学欧文分校（一所西班牙裔服务机构）计算科学和工程研究的跳板。受物理启发的方法的基本假设是，湍流的低成本数字表示可以通过利用限制自然界动态复杂性的物理过程以一种特别有利的方式生成。对于紊流来说，最重要的是，这意味着模拟粘度的物理特性来开发一种粗化过程。在最简单的情况下，物理启发和空间过滤方法在数学上是等价的，其中空间过滤已被证明是最有效的。对于更复杂、更现实的情况，如非均匀网格分辨率的流动模拟或固体表面附近的湍流建模，物理启发的方法提供了一种新的建模框架，避免了与空间滤波相关的缺点。该项目将与LES一起进行直接数值模拟，在一系列流动条件下严格测试新模型，包括各向同性湍流、无壁剪切流动和有壁流动。评估将包括在实施之前对模型准确性的直接测试，以及在LES中对模型性能的综合测试。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Fluid turbulence constitutes a key physical phenomenon with vital implications in a wide range of engineering and scientific fields. However, turbulent flows are notoriously costly to simulate and predict due to their essentially nonlinear, chaotic behavior involving a wide range of coupled length and time scales. An increasingly attractive method is to compute only the dynamics of large-scale motions with models to represent the net effect of unresolved features, an approach known as Large-Eddy Simulation (LES). The underlying theory of LES based on spatial filtering, however, suffers from several shortcomings, including the lack of an accurate, consistent treatment of nonuniform grid resolution, boundaries, and interfaces. This proposal introduces the idea of physics-inspired coarsening as a potentially transformative concept for addressing these challenges. The main objective of the project is to develop the physics-inspired framework for turbulent flow simulations and to test it on representative flows sharing the essential characteristics with many turbulent flows of interest. As such, the proposed work aims to develop game-changing simulation technologies relevant to applications including oceanography, atmospheric science, renewable energy, aerospace, propulsion, astrophysics, and even human health. The project will include the development of a new undergraduate course in numerical methods and a fully integrated undergraduate research project to serve as on-ramps to computational science and engineering research at UC Irvine, a Hispanic Serving Institution.The essential hypothesis of the physics-inspired approach is that low-cost digital representations of turbulent flows can be generated in a particularly advantageous way by leveraging physical processes that limit dynamical complexity in nature. Of foremost importance for turbulent flows, this means mimicking the physics of viscosity to develop a coarsening procedure. The physics-inspired and spatial filtering approaches are mathematically equivalent in the very simplest of cases, where spatial filtering has proven most effective. For more complex, realistic cases such as flow simulations with non-uniform grid resolution or turbulent flow modeling near a solid surface, the physics-inspired method provides a novel modeling framework that avoids the shortcomings associated with spatial filtering. The project will perform Direct Numerical Simulations together with LES to rigorously test new models in a range of flow conditions including isotropic turbulence, wall-free shear flows, and wall-bounded flows. Evaluations will include both direct testing of model accuracy prior to implementation as well as integrated testing of model performance within LES.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.