弹性动脉局部狭窄血管内血流的ALE有限元分析-应用数学专业论文.docxVIP

PAGE PAGE iii 5.3.1血流速度随时间变化分析 30 5.3.2压力随时间变化分析35 5.4本章小节37 第六章 总结与展望38 6.1研究工作总结38 6.2展望38 参考文献40 附录（成果目录）44 致谢 45 摘要 生物流体力学是流体力学与生物学、医学等多种学科之间相互渗透的边缘学科。它 依据经典力学、流体力学的知识来了解生命科学中的某些现象，用力学的方法定量地分 析研究生命系统的功能和构造之间的关系，进而探讨生命现象的运动规律。在生物流体 力学研究中，采用数值计算或数值模拟已成为重要的研究手段。 本文具体内容是针对狭窄动脉血管中血液的流动状况，采用任意拉格朗日—欧拉方 法(ALE),模拟了二维弹性动脉血管内血液流动的情况，并用有限元方法对刚性狭窄血管 内的血流情况进行了数值模拟。在给定相同的边界条件和初值条件下模拟出了弹性血管 和刚性血管中血流速度和压力的变化情况，并且进行比较。并继续分析了不同狭窄程度 的模型的血流状态。结果表明：在刚性狭窄血管中速度和压力随着流场的延长变得非常 不稳定。弹性狭窄血管中由于管壁的弹性，血流的速度和压力要比刚性血管内的变化减 小明显，在通过狭窄后血流情况稳定，更加接近正常生理状况。在正常情况下，人体内 动脉血管中心处流速最快，越往管壁处流速越慢。在血管狭窄部位则为高速层流，且该 高速区流速随狭窄程度加重而加快。所以，对血流动力学的分析将会更好的了解血栓形 成的机理，同时也说明了 ALE 方法对血液流动的数值研究是可行的. 关键词：ALE 方法；有限元法；弹性动脉；局部狭窄；血液流动 ALE Finite Element Analysis of Blood Flow in Stenotic Elastic Arteries ABSTRACT Biofluid mechanics is a cross science which integrates Fluid Mechanics with Biology and Medicine.It discusses some phenomena of life science according to classical mechanics and fluid mechanics,analyses the relation between function and structure of life-system quantificationally and then discusses the motion law on life.So numerical computation and numerical simulation have become important methods on the research of Biofluid mechanics. By means of ALE method,we simulate two-dimensional blood flow through a stenotic elastic artery,also,we simulate the blood flow through a stenotic rigid artery under the same confine condition.The results of the two models are compared.Simulations results show that the velocities and pressure are not stable for the extension of field in rigid artery.Otherwise,because of flexibility of wall the changes of the velocities and pressure in flexible vessel are apparently smaller,and the velocities and pressure of blood flow are stabler,which is more similar to physiological situation.The velocities of blood flow in the normal vessel are different in every stratum, and the velocities are faster in the center and slow down towards the vessel wall.In the field where the vessel is narrowe