形状梯度法求解不可压缩流的形状优化问题

Function Space Parameterization Technique for Shape Optimization Problem of Incompressible Fluid

流体中物体形状优化设计在实践中有重要的应用。对于区域内由Navier-Stokes方程描述的流体,本文研究以流体状态的泛涵为目标函数的优化问题。基于共轭方法与函数空间参数化方法,本文得到了问题的形状导数。在此基础上构造了一种共轭梯度算法。数值例子表明本文的方法是可行的和稳定的。

The shape optimal design for fluid is very important in applications. For a fluid in a region described by a Navier-Stokes equation, our cost fuction is a functional of states of the fluid. Based on the adjoint method and a parametrization method, a formulae of the shape derivatives is established for the problem. Then a conjugate-graduate algorithm is proposed. The numerical examples show the effectiveness and stability of the algorithm.