变分水平集方法在Stokes问题形状识别中的应用

Shape Identification for Stokes Problem Using Variational Level Set Method

对二维定常Stokes方程的形状识别问题进行了研究.直接从变分原理出发,将经典的形状灵敏度分析方法与水平集方法相结合,提出了一种可以适用于流体形状识别的新算法.该算法是在固定的Euler网格上进行计算且在优化过程中不需要对水平集函数进行重新初始化,从而节省了计算时间.所提供的数值算例验证了所提算法是稳定、高效的.

A shape identification for steady-state Stokes problem is considered. Following the variational principle, an algorithm by integrating the classical shape sensitivity analysis with the level set method to suit to shape identification in fluid flow. The cost of this algorithm is moderate since the shape is captured on a fixed Eulerian mesh and the re-initialization procedure is optional during the optimization process. The numerical examples are given to illustrate the promising features of the present method in stabilization and efficiency.