工程数学学报
工程數學學報
공정수학학보
CHINESE JOURNAL OF ENGINEERING MATHEMATICS
2012年
3期
437-450
,共14页
形状优化设计%定常Stoke方程%对流传热%流体耦合问题%形状梯度
形狀優化設計%定常Stoke方程%對流傳熱%流體耦閤問題%形狀梯度
형상우화설계%정상Stoke방정%대류전열%류체우합문제%형상제도
shape optimal design%steady-state Stokes equations%convective heat transfer%fluid coupling problem%shape gradient%gradient algorithm
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.
本文研究瞭耦閤對流傳熱的Stokes流體中的形狀優化問題.利用不可壓縮的定常Stokes方程耦閤對流傳熱的模型來描述流體的特性,運用形狀導數方法分析依賴于區域的狀態方程解的極小化問題.通過引入共軛狀態方程,計算齣目標函數的微分形式,併構造求解該形狀優化問題的梯度型算法.數值實驗的結果驗證瞭所用方法的有效性和可行性.
본문연구료우합대류전열적Stokes류체중적형상우화문제.이용불가압축적정상Stokes방정우합대류전열적모형래묘술류체적특성,운용형상도수방법분석의뢰우구역적상태방정해적겁소화문제.통과인입공액상태방정,계산출목표함수적미분형식,병구조구해해형상우화문제적제도형산법.수치실험적결과험증료소용방법적유효성화가행성.
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.
