自由界面问题的拉格朗日粒子和流体体积耦合算法

针对自由界面问题，构建了拉格朗日粒子和流体体积(volume of fluid， VOF)耦合算法.拉格朗日粒子方法可以准确追踪运动界面，但是一般很难保证流体的质量守恒性.VOF方法可以保证很好的质量守恒性，但是不容易计算界面的几何信息.因此，本文构造了一种耦合算法，吸收两种方法的优点.耦合算法中还引入了四叉树自适应网格技术，可以在大变形区域提高界面的分辨率，并能减少计算量.利用耦合算法模拟经典的Zalesak旋转盘问题和单涡剪切流动，数值结果和文献已有结果吻合较好，验证了耦合算法的稳定性、有效性和准确性.

Coupled Algorithm of Lagrangian Particle Method and Volume of Fluid Method for Free Interface Problem

For free interface problem， a coupled algorithm of Lagrangian particle method and volume of fluid(VOF) was proposed. Although the Lagrangian particle method is able to accurately capture the interface front， there is no mechanism to guarantee the mass conservation. The volume of fluid method is known for its good mass conservation property. However， it is not easy to calculate the geometrical information of the interface. In the coupled method， the advantages of these two methods were combined. The technique of quad-tree adaptive grid was also added， which is able to track interface with high resolution and also save the computational cost. The traditional examples， i.e.， Zalesak’s slotted disk and reversed single vortex flow， are employed to illustrate the stability accuracy and efficiency of our coupled algorithm for solving dynamic interface problems. The numerical results agree with the existing results in the literature.