Numerical Analysis of Large Eddy Simulation

9972622该建议是大涡模拟数学发展的开始。大涡模拟（或LES）试图预测流体湍流中大型结构的运动。 大涡模拟自1970年问世以来，得到了工程计算流体力学界的高度发展。本建议是提供一个数学和数值分析的基础领域。具体而言，它包括：建模-改进的空间过滤流模型的推导，渐近-这种模型的改进的边界条件，分析-建模误差的严格分析研究，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LES新方法，模拟-对所研究的模型和算法进行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问题这些应用包括：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）;以及生物物理学应用（心脏，特别是左心室中的血液流动）。 湍流是由称为涡流的旋涡流体的相干斑块组成的。 它们的大小不等，从飓风等大型风暴系统到蝴蝶翅膀上的小漩涡。大涡模拟（简称LES）旨在预测与小涡解耦的最大和最重要的涡的运动。 这种解耦是很重要的，因为大的漩涡可以在计算网格（物理问题的块的集合）上解决，这可以由超级计算机处理。 拟议的研究重点是模拟湍流中的大涡（如风暴锋面，飓风和龙卷风），在计算实验中预测它们的运动，并在数学上验证大涡模型和算法的发展。 目前的方法LES目前似乎面临着一些障碍，分辨率，准确性和可预测性。 这些障碍中有许多似乎可以追溯到所用模型的数学基础、所施加的边界条件和模拟所采用的算法。 所进行的研究是开发这些数学基础作为指导实际的高性能计算。 这项研究有望扩大预测的准确性和可靠性的范围，这些预测对上述应用很重要，因为技术进步需要面对湍流。

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.