基于ALE方法的3D充填流动模拟

Numercal simulation of three dimensional mold filling flow using Arbitrary Lagrangian Eulerian finite element method

基于任意拉格朗日-欧拉方法发展了三维充填流动的数值模拟方案。该方案采用ALE方法准确地追踪移动自由面的位置并避免了网格扭曲;基于移动最小二乘曲面拟合方法提出了移动自由面上网格节点重定位方法,将充填流动的网格更新过程简化为自由面附近的局部网格重划分过程,并通过分级多面体三角剖分实现,减小了网格划分的计算量,实现了实时网格生成。给出的数值算例结果表明了该数值模型对三维充填流动模拟的有效性。

This paper presents a scheme for numerical simulation of the three dimensional free surface flow in mold filling process by using Arbitrary Lagrangian Eulerian （ALE） finite element method. In light of the ALE description, the moving free surface is accurately tracked without the emergence of en- tangled elements due to the relative movement of free surface nodes. Based on the moving least square （MLS） surface fitting method, a re-positioning technique is proposed for adjusting nodes on the moving free surface with complex shape, which determines the movement of free surface nodes in a self-adaptive manner. By virtue of the ALE method, the mesh regeneration frequently required in free surface flow problems is converted into a local remeshing process in the vicinity of the moving free surface, and implemented by the proposed hierarchical polyhedron triangulation technique. The interpolation errors in- volved in the remeshing process are minimized and only occur in local zones, and the computational effort of the remeshing process is reduced greatly and the real-time mesh generation is available. Examples of the three dimensional mold filling simulation are presented to illustrate the capability of the numerical scheme.