【作者】 李林；

【导师】 林平；

【作者基本信息】 北京科技大学 ， 一般力学与力学基础， 2017， 博士

【摘要】 流体在胀缩渗透管道内的二维流动问题,无论在理论研究方面还是实际应用方面都有重要价值。越来越多的研究证据表明,管道壁面的胀缩性与渗透性对管内流体流动的形成与发展起着关键作用。但时至今日胀缩渗透因素确切的作用还需进一步了解。近年来这也是流体力学的一个研究热点。因此,更深入地研究这类管道内的流动问题对于理解胀缩渗透在流动控制方面的作用有重要意义。本文基于计算数学、物理及流体力学等众多领域中的最新进展及成果,走渐近解与数值解相结合的技术方法和路线,从牛顿流体在胀缩渗透管道内的流动问题出发,研究内容主要集中在微分方程的奇异性、渐近解求高阶导之后出现的奇异性及寻找多解等问题上。当考虑到血管内的血液是非牛顿流体时,则在牛顿流体的研究基础之上,进一步研究了微极性流体在胀缩渗透圆形管道内的流动问题。为了突出研究重点,本文主要呈现了多解和流速的模拟求解及分析处理结果上。更重要的是计算模拟的结果与已有文献中的结果及渐近解结果有着很好的吻合,这证实了本文中所获的结果是正确、有效的。其次,本文中所获得的创新性研究成果归纳在第六章中。最后,本课题的研究目的在于,通过数值结果与渐近结果的比较与分析,以期在这类流动问题中做些基础而有实际价值的工作。本课题研究的意义还在于,对胀缩渗透管道内的流动进行流体力学和计算数学的综合研究,弥补纯流体力学或计算数学化的研究不足,全面揭示这类流动存在地各各方面的问题。因此,本项目将有着良好且广泛的应用前景,它不仅提供了寻找微分方程多解的数值技术、替代不常规边界条件和处理奇异点的理论分析过程,而且还阐释了相应的物理机制,可进一步理解此类问题的流动规律。更多还原

【Abstract】 Two-dimensional flow in a porous pipe with expanding or contracting wall has important value in theoretical studies and practical applications.There is more and more evidence that the swell-shrink and porous characteristics of the pipe wall play an important role in the development of the fluid flow.But even up to now,the specific role of the swell-shrink and porous characteristics is not well understood yet and it has drawn lots of research focus during the last decades.Therefore studies on the flow in a porous pipe with expanding or contracting wall are significantly meaningful to understand the effects of the swell-shrink and porous characteristics on an efficient flow control method.With help from the latest results in research of numerical mathematics、physics and fluid mechanics and the combination of numerical and asymptotic solutions,this paper begins with laminar flow of Newtonian fluid in a porous circular pipe with expanding or contracting wall.When considering the blood in the vessel is non-Newtonian fluid and the research work on Newtonian fluid,a study of micropolar fluid flow in a porous circular pipe with expanding or contracting wall is investigated.To highlight research priorities,this paper mainly considers numerical simulation and theoretical analysis on multiple solutions and flow velocity.Moreover,numerical results agree well with asymptotic results,which shows that the results presented in this paper is right.Finally,innovative points and conclusions are included in the sixth chapter.In addition,the aim of this project is that based on the advantage of numerical or applied mathematics and the comparison of numerical and asymptotic results to obtain some fundamental and practical work.This paper also considers a comprehensive research in fluid mechanics and numerical mathematics,which makes up the inadequacy of fluid mechanics(or numerical mathematics)alone.It not only provides a new numerical technique and the process with treating the singular point,but also illustrates the corresponding mechanism,which is helpful to understand the current problems.更多还原