UCM流体的最小二乘有限元解法

Least-square finite element method for Upper-Convected Maxwell flow

提出了求解UCM流体的最小二乘有限元方法。将稳态不可压缩蠕动流的UCM本构方程,利用速度和应力的近似值进行线性化。建立由所有方程残量的L2范数加权和构造的目标泛函,将微分方程组的求解转化为目标泛函的极小化问题。利用目标泛函对应的欧拉-拉格朗日方程建立迭代格式,最后使用有限元方法求解迭代方程。

A least - squares finite element method for upper - convected Maxwell flow is proposed. The constitutive equation of a steady - state incompressible creeping model is linearized by using the approximations of velocity and stress. Least - squares functional involve the L2 - norm of the residuals of each equation multiplied by a proper weight. The problem is transformed into minimize this func- tional. Euler- Lagrange equation corresponding to the least -squares functional is used to obtain the iterative equation. Finally this equation is solved by finite element method.