Numerical Analysis of Large Eddy Simulation

9972622这一提议是对大涡模拟数学发展的开始。大涡模拟(LES)试图预测大型结构物在流体湍流中的运动。自1970年创立以来，大涡模拟得到了工程计算流体力学领域的高度发展。目前的建议是为该领域提供一个数学和数值分析基础。特别是，它包括：改进的空间过滤流动模型的建模-推导，此类模型的渐近-改进的边界条件，分析-严格的建模误差分析研究，数值分析-空间过滤模型算法的推导和验证，直接模拟-大涡直接模拟的大涡模拟的新方法，模拟-计算测试和正在研究的模型和算法的基准。理解湍流是许多重要问题的核心，包括环境和能源相关的应用(全球变化，发动机中燃料和氧化剂的混合和减阻)，空气动力学(喷气式飞机的机动飞行)和生物物理应用(心脏，特别是左心室的血液流动)。湍流是由被称为旋涡的连贯的旋涡流体斑块组成的。它们的大小不一，从飓风这样的大型风暴系统到蝴蝶翅膀上喷出的小漩涡。大涡模拟(简称大涡模拟)致力于预测最大、最重要的涡旋的运动。这种解耦很重要，因为大涡可以在计算网格(物理问题的大块集合)上解决，而计算网格可以由超级计算机处理。本文的研究重点是对湍流中的大涡(如大气中的风暴锋面、飓风和龙卷风)进行模拟，在计算实验中预测它们的运动，并对所开发的大涡模型和算法进行数学验证。目前对大涡模拟的方法似乎在分辨率、准确性和可预测性方面面临一些障碍。这些障碍中的许多似乎都可以追溯到所使用的模型的数学基础、施加的边界条件和用于模拟的算法。所进行的研究旨在发展这些数学基础，以指导实际的高性能计算。这项研究承诺有可能扩大预测的准确性和可靠性范围，这些预测对应用很重要，例如上面描述的那些，在这些应用中，技术进步需要对抗湍流。

9972622This proposal is to begin the mathematical development of large eddy simulation. Large eddy simulation (or LES) tries to predict the motion of the large structures in the turbulent flow of a fluid. LES has been highly developed by the engineering computational fluid dynamics community since its inception in 1970. The present proposal is to provide a mathematical and numerical analytic foundation for the field. In particular, it includes: modeling-derivation of improved space filtered flow models, asymptotics- improved boundary conditions for such models, analysis-rigorous analytical study of the modeling error, numerical analysis-derivation and validation of algorithms for space filtered models, direct simulation- a new approach to LES of direct simulation of large eddies, simulation- computational testing and benchmarking of the models and algorithms under study.Understanding turbulent flow is central to many important problems including environmental and energy related applications (global change, mixing of fuel and oxidizer in engines and drag reduction), aerodynamics (maneuvering flight of jet aircraft) and biophysical applications (blood flow in the heart, especially the left ventricle). Turbulent flow is composed of coherent patches of swirling fluid called eddies. These range in size from large storm systems such as hurricanes to the little swirls of air shed from a butterfly's wings. Large Eddy Simulation (LES for short) seeks to predict the motion of the largest and most important eddies uncoupled from the small eddies. This uncoupling is importantbecause the large eddies are resolvable on a computational mesh (a collection of chunks of the physical problem) which can be handled by a supercomputer. The proposed research centers on modeling the large eddies (such as storm fronts, hurricanes and tornadoes in the atmosphere) in turbulent flow, predicting their motion in computational experiments and validating mathematically the large eddy models and algorithms developed. Current approaches to LES seem to be presently confronting some barriers to resolution, accuracy and predictability. It seems likely that many of these barriers can be traced to the mathematical foundation of the models used, the boundary conditions imposed and the algorithms employed for the simulations. The research undertaken is to develop these mathematical foundations as a guide for practical high performance computation. This research promises to make it possible to extend the range of accuracy and reliability of predictions important to applications, such as those described above, where technological progress requires confronting turbulence.