中文摘要：

设计和推导了一个用以模拟粘弹性流动问题的混合型有限元方案I_PS_DEVSS_CNBS。在基于Crank-Nicolson隐式差分离散的迭代型分步算法框架内，引入有限增量（FIC）压力稳定方法和离散粘弹应力分裂方法（DEVSS），分别用于克服空间压力振荡和弹性失稳现象，本构方程采用非一致流线上风算法（SU）离散。该方案可允许在粘弹性流动问题中稳定有效地采用所期待的应力-速度-压力变量的等低阶插值单元。方法的有效性将通过平面Poiseuille流进行验证。

英文摘要：

A mixed finite element scheme abbreviated as I_PS_DEVSS CNBS scheme for modeling viscoelastic flow problems is presented. The finite incremental calculus （FIC） pressure stabilization process and the discrete elastic-viscous stress-splitting method （DEVSS） are introduced into the general framework of the iterative version of the fraction- al step algorithm with the use of the Crank Nicolson-based splitting. Inconsistent streamline upwinding method （SU） is employed to spatially discretize the constitutive equation of visco- elastic fluids. Equal low-order finite elements which violate the LBB compatibility condi- tions are successfully used in the proposed scheme. In addition, the proposed scheme will be verified in the plane Poiseuille flow problem quantitatively.