中文摘要：

基于充模过程的两相黏弹性流体模型,采用有限体积、浸入边界和复合水平集流体体积方法,数值模拟了聚合熔体在复杂型腔中的充模过程.首先,借助一类特殊函数（R-functions）将基于基本几何体的水平集函数组合成描述复杂型腔的形状水平集函数.然后,采用浸入边界法处理复杂型腔问题,有限体积方法求解熔体控制方程,利用复合水平集流体体积方法对熔体前沿界面进行隐式追踪.基于有限伸展非线性弹性哑铃本构方程模型,计算熔体分子构型张量,通过取向椭圆描述分子的取向及拉伸行为,实现了充模过程中分子构型的可视化.最后,对带有两个圆形嵌件的环状型腔内的充模过程进行数值模拟研究,得到了充模过程中型腔内的温度、应力及分子构型的变化情况,并重点分析了充模速度、熔体温度和模具温度等对分子构型的影响.数值结果表明：本文提出的耦合模型可以成功模拟复杂型腔内充模过程中的温度、应力和分子取向等物理量的动态变化;适当提高注射速度可以增大熔接痕的强度;提升熔体温度和模具温度,可以有效改善甚至消除熔接痕.

英文摘要：

In the mold filling process,polymer melt will suffer the shear stress and stretch,which has important influences on the mechanical properties and surface quality of the final plastic products.In this paper a gas-liquid two-phase flow model for a viscoelastic fluid is proposed and used to simulate the mold filling process,in which the finitely extensible nonlinear elastic dumbbell with Peterlin closure（FENE-P） model and cross-WLF viscosity model combined with Tait state equation are used to describe the constitutive relationship and viscosity change of the viscoelastic melt,respectively.Meanwhile,the improved coupled level-set and volume-of-fluid method is used to trace the melt front,and the finite volume method on non-staggered grid is used to solve the mass,momentum,and energy conservation equations.Firstly,the R-function,an excellent implicit modeling tool of constructive solid geometry,is employed to establish the shape level-set function to describe the complex mold cavities based on the signed distance functions that represent basic geometries.And the immersed boundary method is applied to dealing with the complex mold cavities by using the shape level-set function.The benchmark problem of the flow past a cylinder is simulated to verify the validity of the FENE-P model,where the orientational ellipses are used to describe the molecular orientation and deformation.Moreover,the visualization of polymer molecular deformation is achieved.Then,the non-isothermal filling process of the viscoelastic fluid is simulated in an annular mold cavity with two circular insets,and the behaviors of the molecular orientation,temperature and stress in the filling process are shown and analyzed in detail.Finally,the problems are also discussed that how the injection velocity,melt and mold temperatures influences on the molecular conformation and solidified layer thickness.Numerical results show that the computational framework proposed in this paper can be successfully used to simulate the non-isothermal mold filling proce