一种改进的水平集方法在Navier-Stokes问题形状优化中的应用

An Improved Level Set Method for the Shape Optimization of Navier-Stokes Problems

本文将经典的形状灵敏度分析方法与一种改进的水平集方法相结合,给出了Navier-Stokes问题形状优化的一种新方法。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,从而可以有效地节省计算时间。数值算例说明该算法是稳定、高效的。

Based on the classical shape sensitivity and the variational principle, a new level set method is proposed for the optimal shape control of the steady-state Navier-Stokes fluid flow. The cost of this method is moderate since the shape is captured on a fixed Eulerian mesh. Furthermore, unlike the classical level set method, the re-initialization procedure is not necessary during the optimization process. Promising features of the proposed method are illustrated by several numerical examples.