耦合对流传热的Stokes流体形状优化设计(英文)

Optimal Shape Design in a Stokes Flow with Convective Heat Transfer

本文研究了耦合对流传热的Stokes流体中的形状优化问题.利用不可压缩的定常Stokes方程耦合对流传热的模型来描述流体的特性,运用形状导数方法分析依赖于区域的状态方程解的极小化问题.通过引入共轭状态方程,计算出目标函数的微分形式,并构造求解该形状优化问题的梯度型算法.数值实验的结果验证了所用方法的有效性和可行性.

This paper is concerned with a shape optimal design problem for a convective heat transfer flow described by the steady-state Stokes equations coupled with a thermal model. The problem consists in minimizing a cost functional which depends on the solution with respect to the domain of the state equations. We calculate the expression of the exact differential for the cost functional by the adjoint state equations, and propose a gradient type algorithm to solve the shape optimal design problem. Numerical examples indicate that our method is efficient and feasible in practical implementations.