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 - <p style="text-align: justify;">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.</p>