流体拓扑优化的参数选择与分析

董馨; 刘小民

doi:10.7652/xjtuxb201808020

您当前的位置：

首页 >

文章列表页 >

流体拓扑优化的参数选择与分析

更新时间：2025-07-09

- 流体拓扑优化的参数选择与分析
- Selection and Analysis of Parameters for Fluid Topology Optimization
- 西安交通大学学报 2018年52卷第8期页码：132-138
- 作者机构：
  
  西安交通大学能源与动力工程学院,西安,710049
- 作者简介：
- 基金信息：
  
  : 2018-01-08。作者简介: 董馨(1995—),女,博士生;刘小民(通信作者),男,教授,博士生导师。基金项目: 国家自然科学基金资助项目(51676152)
- DOI：10.7652/xjtuxb201808020
  中图分类号： O351.2
- 网络首发：2018-08-10，
  
  纸质出版：2018
- 稿件说明：
移动端阅览
董馨, 刘小民. 流体拓扑优化的参数选择与分析[J]. 西安交通大学学报, 2018,52(8):132-138.

Selection and Analysis of Parameters for Fluid Topology Optimization[J]. 2018, 52(8): 132-138.
董馨, 刘小民. 流体拓扑优化的参数选择与分析[J]. 西安交通大学学报, 2018,52(8):132-138. DOI： 10.7652/xjtuxb201808020.

Selection and Analysis of Parameters for Fluid Topology Optimization[J]. 2018, 52(8): 132-138. DOI： 10.7652/xjtuxb201808020.

摘要

针对低雷诺数条件下翼型拓扑优化问题

基于改进的水平集方法研究了流体拓扑优化过程中参数选择对计算速度和结果准确性的影响。引入新参数m描述每次迭代时水平集函数进化的次数

用以控制进化的准确性与计算速度; 通过数值推导选取适当的时间步长系数k

获得了影响数值计算收敛性及速度的参数选取规律。模拟计算研究结果表明:较大的m和k会导致计算收敛不稳定

无法获得精确的收敛数据; 较小的m和k值会降低计算速度。分别建立m和k与迭代步数的函数

在满足优化准确性的前提下

可将收敛速度分别提高85%和80%

同时改进m和k的选取方式

可将收敛速度提高96%

采用改进的水平集拓扑优化方法有效地提高了计算收敛速度和收敛精度。

Abstract

Influences of parameter selection on the calculation speed and the accuracy of the results in the process of fluid topology optimization are studied for the airfoil topology optimization problem with low Reynolds number on the basis of the improved level set method. A new parameter m is introduced to describe the evolution times of the level set function in every iterative step and to control the accuracy and speed of evolution. An appropriate time step coefficient k is selected by numerical derivation

and the parameter selection rules that affect the convergence and speed of the numerical calculation are obtained. Results show that larger values of m and k will lead to unstable convergence and inaccurate convergence data

while smaller values of m and k will reduce the calculation speed. Functions of the parameters m and k and iterative steps are established

respectively

and the convergence speed increases by 85% and 80%

respectively on the premise of satisfying the accuracy of optimization. When selection ways of m and k are improved at the same time

the convergence speed will increase by 96%.

关键词

Keywords

references

OSHER S, SETHIAN J A. Fronts propagating with curvature-dependent speed: algorithms based on Hamilt-Jacobi formulations [J]. Journal of Computational Physics, 1988, 79(1): 12-49.

任晓辉, 封建湖. 基于水平集方法的连续体结构拓扑优化 [J]. 建筑科学与工程学报, 2007, 24(1): 74-79.

REN Xiaohui, FENG Jianhu. Topology optimization of continuum structure based on level set method [J]. Journal of Architecture and Civil Engineering, 2007, 24(1): 74-79.

段献葆, 秦新强. 一种改进的水平集方法在Navier-Stokes问题形状优化中的应用 [J]. 工程数学学报, 2010, 27(2): 242-248.

DUAN Xianbao, QIN Xinqiang. An improved level set method for the shape optimization of Navier-Stokes problems [J]. Chinese Journal of Engineering Mathematics, 2010, 27(2): 242-248.

张彬, 刘小民. 一种保持界面位置不动的水平集函数隐式重新初始化方法 [J]. 计算物理, 2011, 28(5): 667-676.

ZHANG Bin, LIU Xiaomin. An implicit re-initialization method for level set function keeping interface fixed [J]. Chinese Journal of Computational Physics, 2011, 28(5): 667-676.

DUNNING P D, STANFORD B K, KIM H A. Coupled aerostructural topology optimization using a level set method for 3D aircraft wings [J]. Structural Multidisciplinary Optimization, 2015, 51(5): 1-20.

DUAN X, LI F, QIN X. Topology optimization of incompressible Navier-Stokes problem by level set based adaptive mesh method [J]. Computers Mathematics with Applications, 2016, 72(4): 1131-1141.

YAMASAKI S, YAMANAKA S, FUJITA K. Three-dimensional grayscale-free topology optimization using a level-set based r-refinement method [J]. International Journal for Numerical Methods in Engineering, 2017, 112(10): 1402-1438.

刘小民, 张彬, 张卓飒. 水平集与灵敏度分析相结合的流体形状识别与优化方法 [J]. 西安交通大学学报, 2014, 48(7): 5-11.

LIU Xiaomin, ZHANG Bin, ZHANG Zhuosa. Fluid shape recognition and optimization by combining level set method with sensitivity analysis [J]. Journal of Xi'an Jiaotong University, 2014, 48(7): 5-11.

OSHER S, SHU C W. High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations [J]. SIAM Journal on Numerical Analysis, 1991, 28(4): 907-922.

BORRVALL T, PETERSSON J. Topology optimization of fluids in Stokes flow [J]. International Journal for Numerical Methods in Fluids, 2003, 41(1): 77-107.

SUSSMAN M, SMEREKA P, OSHER S. A level set approach for computing solutions to incompressible two-phase flow [J]. Journal of Computational Physics, 1994, 114(1): 146-159.

肖昌炎, 赵永明, 张素, 等. 水平集方法中符号距离函数快速重构 [J]. 信号处理, 2003, 19(6): 551-555.

XIAO Changyan, ZHAO Yongming, ZHANG Su, et al. Fast reconstruction of signed distance function in level set method [J]. Single Processing, 2003, 19(6): 551-555.

DUAN X B, MA Y C, ZHANG R. Optimal shape control of fluid flow using variational level set method [J]. Physics Letters A, 2008, 372(9): 1374-1379.

CHANTALAT F, BRUNEAU C H, GALUSINSKI C, et al. Level-set penalization and Cartesian meshes: a paradigm for inverse problems and optimal design [J]. Journal of Computational Physics, 2009, 228(17): 6291-6315.

SOKOLOWSKI J, ZOLESIO J P. Introduction to shape optimization: shape sensitivity analysis [M]. Berlin, Germany: Springer, 1992: 16-20.

浏览量

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

采用拓扑优化液冷与相变材料协同的大圆柱电池热管理

管壳式水合盐化学储热反应器内传热结构拓扑优化

面向金属泡沫散热器设计的自然对流拓扑优化

桁架结构拓扑及截面尺寸优化设计方法

隐式曲面梯度多孔结构拓扑优化设计方法