Numerical Analysis of Large Eddy Simulation

9972622这个建议是开始大涡模拟的数学发展。大涡模拟（Large eddy simulation， LES）试图预测流体湍流中大型结构体的运动。自1970年成立以来，工程计算流体力学界一直高度发展LES。目前的建议是为该领域提供一个数学和数值分析的基础。特别是，它包括：改进的空间过滤流模型的建模-推导，渐近性-改进的模型边界条件，分析-对建模误差的严格分析研究，空间过滤模型的数值分析-推导和算法的验证，直接模拟-直接模拟大涡流的LES的新方法，模拟-模型和算法的计算测试和基准测试。了解湍流是许多重要问题的核心，包括环境和能源相关应用（全球变化，发动机中燃料和氧化剂的混合以及减阻），空气动力学（喷气式飞机的机动飞行）和生物物理应用（心脏中的血液流动，特别是左心室）。湍流是由被称为涡流的连贯的旋转流体块组成的。它们的大小不等，从飓风这样的大型风暴系统到蝴蝶翅膀上的小涡流。大涡模拟（简称LES）旨在预测从小涡中分离出来的最大和最重要的涡的运动。这种解耦是很重要的，因为大涡流可以在计算网格（物理问题块的集合）上解决，这可以由超级计算机处理。本研究以紊流中的大涡流（如风暴锋、飓风和龙卷风）为中心，在计算实验中预测其运动，并在数学上验证所开发的大涡流模型和算法。目前的LES方法似乎在分辨率、准确性和可预测性方面遇到了一些障碍。这些障碍似乎可以追溯到所使用模型的数学基础、所施加的边界条件和所采用的模拟算法。所进行的研究是发展这些数学基础，作为实际高性能计算的指导。这项研究有望扩大预测的准确性和可靠性范围，这些预测对上述技术进步需要面对湍流的应用至关重要。

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.