摘要
计算机符号运算科学是人工智能的前沿方向· 计算机软件Ｍａｃｓｙｍａ 是完成符号运算的有力工具· 应用德国Ｄａｒｍｓｔａｄｔ 大学的计算机软件Ｍａｃｓｙｍａ、与数学方法和流变学模型结合，研究了Ｏｌｄｒｏｙｄ Ｂ流体由一类定常状态向另一定常状态转变的非定常流动过程· 采用改进的Ｋａｎｔｏｒｏｖｉｃｈ 方法和符号运算软件，把该问题的３ 阶偏微分方程的初、边值问题化为各级近似的２ 阶常微分方程问题· 并给出了１ 级、２ 级和３ 级近似方程的解析形式解答· 该研究表明了计算机符号处理解决应用数学和力学问题的潜力，同时指出了由一定常状态向另一定常状态转变的非牛顿流动过程，可以经历无限多途径。
A combination of the computational symbolic calculation, mathematical approach and physico_mechanical model leads to a computational intellectual analytical approach developed by the author. There is a principal difference between the computer proof and the computer derivation completed by the computer,also difference between the numerical and symbolic calculations. In this investigation the comutatiinal analytical approach is extended,and an unsteady flow of non_Newtonian fluid is the gap between two rotating coaxial cylinders is studied. The Oldroyd fluid B model is used by which the Weissenberg effects are explained in a good comparison with the experiments. The governing equations are reduced to a partial differential equation of 3rd order for the dimensionless velocity. Using the computer software Macsyma and an improved variational approach the problem with the initial and boundary conditions are then reduced to a problem of an ordinary differential equation for different approximations. The analytical solutions are given for the 1st, 2nd 3rd approximations. The present investigation shows the ability of the computational symbolic manipulation in solving the problems of non_Newtonian fluid flows. There is a possibility of that to solve the problems in the mathematics and the mechanics. An important conclusion can be drawn from the results that the transition from a steady state to another steady state is non_unique.
出处
《应用数学和力学》
EI
CSCD
北大核心
1999年第11期1149-1160,共12页
Applied Mathematics and Mechanics
基金
国家自然科学基金
德国洪堡基金
关键词
计算机符号运算
旋转流动
非牛顿流体
非定常流
time_dependent rotating flow
non_Newtonian fluid
Oldroyd fluid B
computational symbolic manipulation
computational analytical approach
