中文摘要：

在任意拉格朗日—欧拉（Arbitrary Lagrangian-Eulerian,ALE）方法框架中发展用于成形充填过程数值模拟的有限元与无网格自适应耦合方案。该方案自适应地在网格发生扭曲的区域采用无网格法空间离散以保证求解的精度和稳定性,而在网格质量较好的区域以及本质边界上保留使用有限元法空间离散以提高计算效率和便于施加本质边界条件,从而在充分发掘有限元法和无网格法各自优点的同时避开它们各自的缺点,在一定程度上保证该方法同时具有较快的计算速度和较好的健壮性。采用ALE参考构形描写充填过程中的熔体质量运动及守恒,可在不频繁变动网格的前提下准确跟踪自由面。应用压力稳定型分步算法求解控制方程,可方便采用不满足Ladyzhenskaja-Babuska-Brezzi（LBB）条件的速度、压力的同低阶插值。进行两个典型算例的数值模拟,结果表明该方法相对于单一的有限元法和无网格法的优越性,以及对含自由面变质量体系流动问题数值模拟的有效性。

英文摘要：

An adaptive coupled finite element and meshfree method is developed in the arbitrary Lagrangian-Eulerian （ALE） framework for numerical simulation of injection molding process. In the proposed method the meshfree approximation is adopted in the region where the mesh is distorted to preserve the accuracy and robustness of numerical solutions from the deterioration of the mesh quality, while the finite element approximation is employed in the region where the quality of the mesh is acceptable and on the boundaries where essential boundary conditions of flow problems are imposed to ensure high computational efficiency and proper imposition of the essential boundary conditions. In such a way, the respective strong points of the finite element and meshfree methods are adequately exploited while the respective weak pints of them are effectively suppressed, which makes the present method quite robust as well as efficient to some extent. The description of the mass movement and conservation of the melt polymer in the filling process is referred to the ALE referential configuration, accordingly the free surfaces can be accurately tracked without the need of frequent mesh updates. By virtue of adopting the pressure stabilized fractional step algorithm to solve the governing equations, equal low order velocity-pressure interpolations that violate the so-called Ladyzhenskaja-BabuskaBrezzi （LBB） condition can be conveniently used for the simulation. Numerical results of two typical problems are illustrated to demonstrate the superiority of the proposed method over the solely applied finite element and meshfree methods in overall performance including efficiency, accuracy as well as robustness and its ability for numerical simulation of free surface flow problems with variable mass bulk.