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耦合对流传热的Stokes流体形状优化设计
  • ISSN号：1005-3085
  • 期刊名称：《工程数学学报》
  • 时间：0
  • 分类：O241.82[理学—计算数学;理学—数学]
  • 作者机构：[1]西安交通大学数学与统计学院,西安710049
  • 相关基金：The National Natural Science Foundation of China （10901127; 11171269）; the Science Foundation for the Doctoral Program of Education Ministry of China （20090201120055）.
作者： 晏文璟[1], 侯江勇[1], 马逸尘[1]
关键词： 形状优化设计, 定常STOKES方程, 对流传热, 流体耦合问题, 形状梯度, shape optimal design, steady-state Stokes equations, convective heat transfer, fluid cou-pling problem, shape gradient, gradient algorithm
中文摘要：

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．

英文摘要：

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.

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期刊信息
  • 《工程数学学报》
  • 北大核心期刊（2011版）
  • 主管单位:教育部
  • 主办单位:西安交通大学
  • 主编：李大潜
  • 地址：西宁市咸宁西路28号西安交通大学数学与统计学院
  • 邮编：710049
  • 邮箱：jgsx@mail.xjtu.edu.cn
  • 电话：029-82667877
  • 国际标准刊号：ISSN：1005-3085
  • 国内统一刊号：ISSN：61-1269/O1
  • 邮发代号:
  • 获奖情况:
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  • 被引量:6741