基于伴随方程的网格自适应及误差修正技术研究

发布时间：2018-01-06 03:14

本文关键词：基于伴随方程的网格自适应及误差修正技术研究　出处：《中国空气动力研究与发展中心》2016年硕士论文　论文类型：学位论文

【摘要】：随着计算机运算能力和编程语言的迅速发展,计算流体力学(CFD)发展成为航空航天飞行器气动设计的重要方法之一,在流体力学基础研究与航空航天飞行器设计及优化过程中发挥着越来越重要的作用。飞行器设计对气动特性的高精度计算要求很高,气动特性的高精度计算主要取决于数值方法格式的精度与计算网格的分辨率。非结构网格相比结构网格具有较大的灵活性,没有结构网格的节点之间相互对应关系,可以更好的在流场的敏感区域进行优化,提高网格的局部分辨率从而提高气动特性的计算精度,在网格自适应领域具有很好的应用前景。当前,误差估计技术得到了CFD工作者的很大关注,误差估计技术可以对计算结果的误差进行估计并修正,为进一步提高计算结果的精度提供了可能性。本文基于非结构网格,离散伴随理论和MFlow流场解算器,发展了一种适用于格心格式有限体积法的网格自适应和误差修正技术,将对气动力较为敏感的网格区域进行加密和优化,并用误差修正技术提高气动力的计算精度。在内容安排上,分为如下五个章节:第一章为引言,介绍了基于伴随方程的网格自适应技术和误差估计技术的背景,以及国内外学者在网格自适应技术与误差修正技术方面的研究现状,给出了本文的主要研究内容。第二章为数值模拟方法,本文的气动特性数值模拟,使用成熟的MFlow流场求解器,本章主要介绍了伴随方程的构建与求解方法,基于伴随理论和非结构网格给出了目标函数的误差估计技术,以降低目标函数的剩余误差为自适应与误差修正的目标,构建了综合性自适应参数。第三章为自适应策略,研究得出了一种综合性较好的粗网格剖分方法,基于非结构网格提出了一种适用于格心格式有限体积法的多项式插值方法,并与参考文献中的插值方法做了详细对比。以降低目标函数误差修正后的剩余误差为目标,构建了基于伴随方程的网格自适应判据。研究了自适应后网格的优化方法,包括空间网格光滑方法以及物面网格投影方法等,探索了基于伴随方程的网格自适应及误差修正的流程。第四章为算例验证与分析,本章对ONERA-M6机翼与NACA0012翼型不同状态下的绕流进行了自适应数值模拟,并对升、阻力等目标函数进行了误差修正。对基于伴随方程的网格自适应技术和基于流场特征的网格自适应方法进行了算例对比,给出了两种自适应方法各自的特征。对算例做了深刻的总结与分析,研究了基于伴随方程的网格自适应技术的加密特点以及对目标函数的影响,分析了物面网格投影方法对自适应过程造成的影响,并对普通CFD工程应用中的网格生成提出了建议。第五章为总结与展望,回顾了论文的研究工作,指出了现有工作所存在的不足,展望了今后的研究方向。
[Abstract]:With the rapid development of computer computing ability and programming language, computational fluid dynamics (CFD) has become one of the most important methods for aeronautical and astronautical aircraft aerodynamic design. It plays a more and more important role in the basic research of hydrodynamics and the design and optimization of aeronautical and spaceflight vehicles. The design of aircraft requires high precision calculation of aerodynamic characteristics. The high accuracy calculation of aerodynamic characteristics mainly depends on the accuracy of numerical method and the resolution of computational meshes. Unstructured meshes are more flexible than structural meshes. The nodes without structural meshes can be optimized in the sensitive region of the flow field, and the local resolution of the mesh can be improved, and the computational accuracy of aerodynamic characteristics can be improved. At present, the error estimation technology has been paid great attention by the CFD workers, and the error estimation technology can estimate and correct the error of the calculation results. This paper is based on unstructured meshes, discrete adjoint theory and MFlow flow field solver. In this paper, a mesh adaptive and error correction technique is developed, which is suitable for the finite volume method of lattice center format, which encrypts and optimizes the more sensitive grid area. In the content arrangement, it is divided into the following five chapters: the first chapter is the introduction, which introduces the background of adaptive mesh technology and error estimation technology based on adjoint equation. As well as the domestic and foreign scholars in the grid adaptive technology and error correction technology, the main research content is given. Chapter two is numerical simulation method, the aerodynamic characteristics of this paper numerical simulation. Using the mature MFlow flow field solver, this chapter mainly introduces the construction and solution of the adjoint equation, and gives the error estimation technique of the objective function based on adjoint theory and unstructured grid. In order to reduce the residual error of the objective function as the target of adaptive and error correction, the comprehensive adaptive parameters are constructed. Chapter 3 is the adaptive strategy, and a comprehensive and better rough mesh generation method is proposed. Based on unstructured meshes, a polynomial interpolation method is proposed, which is suitable for the finite volume method of lattice center format. And compared with the interpolation method in the reference, the goal is to reduce the residual error after the error correction of the objective function. The adaptive criterion of mesh based on adjoint equation is constructed, and the optimization methods of adaptive post-grid are studied, including spatial mesh smoothing method and object surface mesh projection method. The flow of adaptive mesh and error correction based on adjoint equation is explored. Chapter 4th is an example for verification and analysis. In this chapter, the adaptive numerical simulation of the flow around the ONERA-M6 wing and the NACA0012 airfoil in different states is carried out, and the lift is obtained. The error correction of the objective function such as resistance is carried out. The mesh adaptive technique based on adjoint equation and the mesh adaptive method based on flow field characteristics are compared. The characteristics of the two adaptive methods are given. The examples are summarized and analyzed, and the encryption characteristics of the adaptive mesh technology based on the adjoint equation and the effect on the objective function are studied. The effect of object surface mesh projection method on adaptive process is analyzed, and suggestions for mesh generation in general CFD engineering applications are put forward. Chapter 5th is a summary and prospect, and the research work of this paper is reviewed. The shortcomings of the existing work are pointed out, and the future research direction is prospected.
【学位授予单位】：中国空气动力研究与发展中心
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：V211.3

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