粘弹性流动数值模拟方法及其在Poiseuille流中的验证  

A new numerical scheme for viscoelastic flow and its verification in Poiseuille problem

作　　者：张一丁[1] 韩先洪[1] 

机构地区：[1]上海交通大学模具CAD国家工程研究中心,上海200030

出　　处：《模具技术》2012年第4期16-19,共4页Die and Mould Technology

基　　金：国家自然科学基金项目(51105247);宁波市重大科技攻关项目(2010B10018)

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。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.

关 键 词：粘弹性流体 有限元法 有限增量法 离散粘弹应力分裂法 

分 类 号：O373[理学—流体力学]