基于谱方法的管内非牛顿流体非定常流动

以上随体Maxwell流体为非牛顿流体介质，探索了一种用谱方法解析处理水平圆管内非牛顿流体非定常流动的方法.该非定常问题归结为一个非线性二阶偏微分方程的求解问题.用谱方法将非线性二阶偏微分方程求解问题化为常微分方程组Chebyshev多项式数的近似问题，用Laplac变换法和本征值方法求解常微分方程组得到问题的解析结果.

Unsteady Flow of Non- Newtonian Fluid in Pipe by Spectral Method

In the present investigation, the unsteady flow of upper - convected Maxwell fluid in a horizontal circularpipe is studied by spectral method. The unsteady problem is mathematically reduced to a partial differential equation ofsecond order. By using spectral method the partial differential equation can be reduced to a system of ordinary differen-tial equations for different terms of Chebyshev polynomials approximations. The ordinary differential equations are solvedby the method of Laplace transform and the eigenvaluemethod that led to an analytical form of the solutions.