An Efficient Iterative Method for the Formulation of Flow Networks

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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.

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