An Efficient Iterative Method for the Formulation of Flow Networks

作     者：Wei Hu Dong Wang Xiao-Ping Wang 

作者机构：Department of MathematicsThe Hong Kong University of Science and TechnologyClear Water BayKowloonHong Kong School of Science and EngineeringThe Chinese University of Hong KongShenzhenGuangdong 518172China. 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2022年第31卷第5期

页      面：1317-1340页

核心收录：

学科分类：07[理学] 0701[理学-数学] 0702[理学-物理学] 

基　　金：supported by the Guangdong Provincial Key Laboratory of Big Data Computing,The Chinese University of Hong Kong,Shenzhen.D.Wang acknowledges support from National Natural Science Foundation of China grant 12101524 the University Development Fund from The Chinese University of Hong Kong,Shenzhen(UDF01001803) X.-P.Wang was supported in part by the Hong Kong Research Grants Council(GRF grants 16308421,16305819,16303318) the University Development Fund from The Chinese University of Hong Kong,Shenzhen(UDF01002028)。 

主　　题：Topology optimization convolution thresholding Darcy-Stokes flow 

摘      要：We propose an efficient iterative convolution thresholding method for the formulation of flow networks where thefluid is modeled by the Darcy–Stokesflow with the presence of volume sources.The method is based on the minimization of the dissipation power in thefluid region with a Darcy term.Theflow network is represented by its characteristic function and the energy is approximated under this representation.The minimization problem can then be approximately solved by alternating:1)solving a Brinkman equation to model the Darcy–Stokesflow and 2)updating the characteristic function by a simple convolution and thresholding step.The proposed method is simple and easy to implement.We prove mathematically that the iterative method has the total energy decaying property.Numerical experiments demonstrate the performance and robustness of the proposed method and interesting structures are observed.