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Volume 31, Issue 5
An Efficient Iterative Method for the Formulation of Flow Networks

Wei Hu, Dong Wang & Xiao-Ping Wang

DOI: 10.4208/cicp.OA-2021-0234

Commun. Comput. Phys., 31 (2022), pp. 1317-1340.

Published online: 2022-05

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  • Abstract

We propose an efficient iterative convolution thresholding method for the formulation of flow networks where the fluid is modeled by the Darcy–Stokes flow with the presence of volume sources. The method is based on the minimization of the dissipation power in the fluid region with a Darcy term. The flow 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–Stokes flow 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.

  • Keywords

Topology optimization, convolution, thresholding, Darcy–Stokes flow.

  • AMS Subject Headings

35K08, 35Q35, 49Q10, 76S05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-31-1317, author = {Hu , WeiWang , Dong and Wang , Xiao-Ping}, title = {An Efficient Iterative Method for the Formulation of Flow Networks}, journal = {Communications in Computational Physics}, year = {2022}, volume = {31}, number = {5}, pages = {1317--1340}, abstract = {

We propose an efficient iterative convolution thresholding method for the formulation of flow networks where the fluid is modeled by the Darcy–Stokes flow with the presence of volume sources. The method is based on the minimization of the dissipation power in the fluid region with a Darcy term. The flow 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–Stokes flow 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2021-0234}, url = {http://global-sci.org/intro/article_detail/cicp/20506.html} }
TY - JOUR T1 - An Efficient Iterative Method for the Formulation of Flow Networks AU - Hu , Wei AU - Wang , Dong AU - Wang , Xiao-Ping JO - Communications in Computational Physics VL - 5 SP - 1317 EP - 1340 PY - 2022 DA - 2022/05 SN - 31 DO - http://doi.org/10.4208/cicp.OA-2021-0234 UR - https://global-sci.org/intro/article_detail/cicp/20506.html KW - Topology optimization, convolution, thresholding, Darcy–Stokes flow. AB -

We propose an efficient iterative convolution thresholding method for the formulation of flow networks where the fluid is modeled by the Darcy–Stokes flow with the presence of volume sources. The method is based on the minimization of the dissipation power in the fluid region with a Darcy term. The flow 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–Stokes flow 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.

Hu , WeiWang , Dong and Wang , Xiao-Ping. (2022). An Efficient Iterative Method for the Formulation of Flow Networks. Communications in Computational Physics. 31 (5). 1317-1340. doi:10.4208/cicp.OA-2021-0234
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