用Level Set方法求解具有自由面的流动问题

为采用Ｌｅｖｅｌ Ｓｅｔ方法来计算有自由的流动问题提出了一种方案，把自由水面视为水和空气的交界面，两种介质用统一的Ｎ－Ｓ方法求解，在自由面两侧分别采用各自的密度和粘性，并在自由面上给以适当的光滑；采用边界元法求解双调和方程来确定距离函数；Ｎ－Ｓ方程用投影法求解，文中给出了二维水池水面振荡和瞬时溃坝问题的算例，可以看出用ＬｅｖｅｌＳｅｔ方法求解有自由面流动问题是有效的。

SIMULATION OF THE FLOW WITH FREE SURFACE BY LEVEL SET METHOD

The Level Set method is applied to simulate the flow with free surface. The free surface is supposed to be the interface of water and air. The N-S equations in the two phases are solved simultaneously to obtain the velocity and pressure fields. The density of air and water are used in the phase of air and water respectively, and the viscosity is treated in the same way. To avoid numerical instability in computation the density and viscosity are smoothed at the interface. The Level Set function is determined by solving a biharmonic equation with boundary integral equation method and the N-S equations are solved by the second order project method. The evolution of the free surface in an oscillating water basin and during dam-break is sim ulated by the Level Set method, the numerical result agrees well with the characteristic solution and the experiment data.