Abstract Traditional modeling methods of the reduced-order model can not be directly applied to fracture-dominated flow in porous media, violating the mass-conservation nature. In this paper, a global reduced-order model for the steady-state flow in fractured porous media based on the embedded discrete fracture model is established for the first time by using the proper orthogonal decomposition combined with Galerkin projection method. Differing from the typical modeling method of the reduced-order model commonly used in the literature, the discrete matrix equations instead of the primary governing equations are projected onto the low-dimensional space formed by the basis functions. The proposed reduced-order model can successfully handle the coupled terms between the matrix and fracture media. The accuracy and robustness of the proposed model are verified for three complex fracture cases with different boundary conditions. The results show that the maximum relative deviation in these three cases is 8.07 × 10−6%, which can be negligible in practical applications. Additionally, the constructed global reduced-order model is more effective than the finite volume method (at least speed-up 10 times) among these test cases.

中文翻译：

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裂缝性多孔介质稳态流动的POD降阶模型研究

摘要 传统的降阶模型建模方法不能直接应用于多孔介质中以裂缝为主的流动，违反了质量守恒性质。本文首次利用适当的正交分解结合伽辽金投影方法建立了基于嵌入式离散裂缝模型的裂缝多孔介质稳态流动的全局降阶模型。与文献中常用的降阶模型的典型建模方法不同，将离散矩阵方程而不是主控制方程投影到基函数形成的低维空间上。所提出的降阶模型可以成功地处理基质和裂缝介质之间的耦合项。针对三种不同边界条件的复杂裂缝情况，验证了所提出模型的准确性和鲁棒性。结果表明，这三种情况下的最大相对偏差为8.07×10-6%，在实际应用中可以忽略不计。此外，在这些测试用例中，构建的全局降阶模型比有限体积法更有效（至少提速 10 倍）。