应用谱方法研究管内非牛顿流体的非定常流动

Spectral Method for Solwing Unsteady Flow of Non-Newtonian Fluid in Tube

本文研究上随体Maxwell流体在水平管内的非定常流动，该问题可归纳为无量纲速度分量的二阶偏微分方程的边初值问题，采用以Chebyshev多项式为基底的谱方法，将该偏微分方程化为二阶常微分方程组的初值问题，采用Laplace变换，求得二阶常微分方程组的解析解。文中提出了用谱方法解非定常流动的新方法，并通过在常压力梯度和周期性压力梯度两种情形下的计算结果，与用差分法和Kantorovich变分法求得的结果进行比较，证明谱方法适合于研究非定常流动。

In the present investigatinn the unsteady flow of upper-convected Maxwel fluid in a horizontal circular pipe is studied by spectral method. The unsteady problem is mathematically reduced to the inital and boundary value problem of a partial differential second order equation. The chebyshev poynomials are chosen to act as the radical of spectral method.The partial differential equation can be reduced to a system of ordinary differential equations. The ordinary differential equation is solved by the laplace tromsform. In this paper, a new method for solying unsteady flow is put forward. The results which are calculated by this method in condition of constant pressure gradient and periodic pressure gradient compare with that by finite difference method and kantorovich method. The comparing results show that spectral method is suitable for studying the unsteady flow problom of non-Newtonian fluid.