Johnson-Segalman流体剪切流动的相平面分析与数值模拟

研究Johnson-Segalman流体的剪切流动行为. 首先分析该模型的定常解, 从稳定的总剪切 应力曲线上可见, 当稳定总剪切应力T取值足够大或足够小时, 方程有惟一定常解; 当T取中间值时, 方程定常解不惟一. 最后, 采用向后差分格式对该模型进行数值模拟.

Phase-plane Analysis and Numerical Scheme of Shear Flow of Johnson-Segalman Fluid

The present paper deals with the shear flow of Johnson-Segalman fluid. On the basis of the analysis of the steady state solutions, it is obtained that a steady-state solution of JS model corresponds to a point on the steady total stress curve at which the total stress is T(X). When T is sufficiently small or sufficiently large , there is a single steady state solution , while there are three steady state solutions when T is intermediate in value. The steady state solution is judged to be stable or unstable in phase plane in this paper. At last , a new numerical scheme is devised by using backward finite difference method to solve JS model.