用于求解流体动力学问题的FHP-Ⅱ格子气自动机及程序实现

发布时间：2018-04-13 21:51

本文选题：格子气自动机 + FHP-Ⅱ模型　；参考：《吉林大学》2017年硕士论文

【摘要】：格子气自动机(LGA)方法自上世纪70年代产生,80年代发展,到如今已有近40年的历史了。它目前已经发展成为偏微分方程和流体动力学数值模拟领域可选择的一种方法。相较于传统的计算流体力学(CFD)数值方法,格子气自动机具有许多特有的优势。如:计算速度快,并行性好,运行过程无误差等。由于这些优点,格子气自动机在上世纪末受到广大科研工作者的关注。但同时它也存在着统计噪音大,难以模拟高Re数等缺陷。科学家们在这些领域方面做了诸多工作,起到了一定的效果。进入新世纪,基于传统格子气自动机思想的量子格子气自动机模型产生了。它所带来的数据处理能力和计算速度的大幅提升需要引起科研工作者的足够重视。本文主要探索FHP-II格子气自动机模型。研究其运行过程、程序实现,数学基础。并利用几个流体动力学常用问题作为算例,验证了FHP-II格子气自动机模拟低Re数流体动力学问题的可行性。本文的结构如下:第一章,绪论部分。主要介绍格子气自动机的发展历史与研究现状。第二章,探索FHP-II格子气自动机的运行规则,程序实现过程。第三章,从数学理论出发,引入假设,探索格子气自动机演化方程与流体动力学Navier-Stokes方程的关联。第四章,使用三个流体动力学常用问题作为算例,验证FHP-II格子气自动机模拟低Re数流体动力学问题的可行性。第五章,给出结论。并对本领域未来的发展方向做出了展望。
[Abstract]:The lattice gas automata (LGA) method has been developed for nearly 40 years since its development in the 1970s.It has been developed into an alternative method in the field of partial differential equations and numerical simulation of fluid dynamics.Compared with the traditional computational fluid dynamics (CFD) numerical method, the lattice gas automata has many unique advantages.Such as: fast calculation, good parallelism, no error in the running process, etc.As a result of these advantages, lattice gas automata has attracted the attention of researchers at the end of last century.But at the same time, it also has statistical noise, it is difficult to simulate the high re number and other defects.Scientists have done a lot of work in these fields and have had some effect.In the new century, the quantum lattice gas automata model based on the traditional lattice gas automata is produced.The great improvement of data processing ability and computing speed should be paid enough attention to by researchers.This paper mainly discusses the FHP-II lattice gas automata model.Study its running process, program realization, mathematical basis.The feasibility of simulating low re number hydrodynamic problems with FHP-II lattice gas automata is verified by using several commonly used hydrodynamic problems as examples.The structure of this paper is as follows: chapter one, introduction.This paper mainly introduces the development history and research status of lattice gas automata.The second chapter explores the operation rules of FHP-II lattice gas automata and the process of program implementation.In the third chapter, the relationship between the evolution equation of lattice gas automata and the Navier-Stokes equation of hydrodynamics is explored by introducing the hypothesis from the mathematical theory.In chapter 4, three commonly used hydrodynamics problems are used as examples to verify the feasibility of FHP-II lattice gas automata in simulating low re number hydrodynamic problems.Chapter five gives the conclusion.The future development direction of this field is prospected.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O35

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