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arXiv · 2510.13429

A domain decomposition approach to pore-network modeling of porous media flow

Shuyu Sun·Zhangchengrui Wang·Lei Zhang·Jijing Zhao
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Abstract

We propose a domain-decomposition pore-network method (DD-PNM) for modeling single-phase Stokes flow in porous media. The method combines the accuracy of finite-element discretizations on body-fitted meshes within pore subdomains with a sparse global coupling enforced through interface unknowns. Local Dirichlet-to-Neumann operators are precomputed from finite-element solutions for each pore subdomain, enabling a global Schur-complement system defined solely on internal interfaces. Rigorous mathematical analysis establishes solvability and discrete mass conservation of the global system. Moreover, we constructively recover classical pore-network models by fitting half-throat conductivities to local Dirichlet-to-Neumann maps, providing a principled bridge between mesh-based and network-based frameworks. Numerical results are presented to demonstrate the validity and effectiveness of the overall methodology.

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Shuyu Sun, Zhangchengrui Wang, Lei Zhang, Jijing Zhao. 2025-10-15. A domain decomposition approach to pore-network modeling of porous media flow. https://arxiv.org/abs/2510.13429

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