【作者】 周士杰；

【导师】 夏健；

【作者基本信息】 南京航空航天大学 ， 流体力学， 2016， 硕士

【摘要】 随着科学技术的日新月异,航空、航天领域迅猛发展。飞行器不仅在外形、结构上突破传统,飞行高度也不断提升。在飞行高度不断增加的同时,气体密度会越来越小,稀薄气体效应也越来越明显。此时,连续介质假设下的Navier-Stokes方程已经不再适用,取而代之的则是高度非线性的Boltzmann方程。数值求解Boltzmann方程存在着巨大的困难,为了方便研究往往需要对方程进行各式各样的假设。为了有效地解决稀薄气体动力学问题,人们先后发展了一系列的方法。在这些求解稀薄气体动力学的众多方法中,由Bird提出的直接模拟Monte-Carlo方法(DSMC)发展尤为迅速。它的应用范围非常广泛,目前已成为研究稀薄气体动力学非常重要的方法之一。本文主要研究高超声速稀薄气体流动中基于切割单元直角坐标网格的DSMC方法及优化技术,致力于发展一套具有较高自动化程度且通用性良好、适用于切割单元以及任意复杂外形的DSMC程序。本文中,首先阐述了分子气体动力学基本原理,为下文对稀薄气体流动进行直接物理模拟奠定基础。其次,通过对与物面相交的正方体网格进行切割处理来保证单元的贴体性,同时采用网格加密技术使物面附近的网格尺度满足要求。这样的直角坐标网格生成方法不仅提高了计算过程中的搜索效率,也保证了物面附近的计算精度。然后,研究了基于切割单元直角坐标网格的DSMC方法的实现与应用,并发展了一种新的相邻单元搜索方法,能够适用于任意形状多面体间的分子搜索。因为DSMC方法是一种以分子为研究对象的统计方法,对计算机资源要求非常高,所以本文最后研究了当地模拟分子代表真实分子数和动态时间步长两种优化技术来提高程序的计算效率,并通过相应的算例证明了这些方法的正确性。更多还原

【Abstract】 As science and technology advances, the technology in Aeronautics and Astronautics field develops rapidly. Aircraft not only break through the tradition in configuration and structure, flight altitude is also rising. With the rising of flight altitude, the gas density is getting smaller and smaller, rarefied gas effect has become increasingly evident. In this case, under the assumption of continuous media Navier-Stokes equation is no longer applicable, and it is replaced by highly nonlinear Boltzmann equation. Using numerical method to solve Boltzmann equation is extremely difficult, in order to facilitate the study of the equation, a variety of hypotheses are often needed. In order to effectively solve the problem of rarefied gas dynamics, it has developed a series of methods. In these methods for solving the rarefied gas dynamics, the direct simulation Monte-Carlo method(DSMC) which was proposed by Bird develops rapidly. It is widely used, and has been one of the most important way for rarefied gas dynamics study. This paper studies the hypersonic rarefied gas flow DSMC Method based on cut-cell Cartesian mesh and is committed to develop a set of high degree of automation and good universality, suitable for cet-cell and any complex shape DSMC program.In this paper, the basic principles of molecular gas dynamics are elaborated firstly, laying the foundation for direct physical simulation of rarefied gas flow. Secondly, through the cut-cell to ensure the body fitted properties of grid cell, while using mesh refinement technique to meet the requirements of mesh scale near the surface. Such a cartesian mesh generation method not only improves the search efficiency, but also ensures the accuracy of the computation near the surface. Then we study the implementation and application of DSMC method based on cut-cell cartesian mesh, and develop a new adjacent cell search method which can be applied to molecules search between polyhedrons with arbitrary shape. Because the DSMC method is a statistical method for the study of molecules, the requirement of computer resources is extremely high. So, this paper finally studies the local simulation molecules represent real molecular number and dynamic time step two optimization techniques to improve the computational efficiency of the program, and prove the correctness of these methods through the calculation example.更多还原