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A Galerkin‐free/equation‐free model reduction method for single‐phase flow in fractured porous media

机译:裂缝多孔介质中单相流量的无格雷基/公式的模型减少方法

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Using traditional high‐fidelity numerical simulation to simulate fluid flow in fractured porous media in a real field remains challenging. It involves a large number of degrees of freedom when matrix and fracture equations are solved. To address this challenge, we propose a Galerkin‐free framework to construct a reduced‐order model (ROM) based on the proper orthogonal decomposition (POD). Compared with the typical POD‐based modeling process commonly used in previous studies, the POD‐ROM can be built without performing the Galerkin projection of flow equations onto the low‐dimensional space spanned by the POD basis functions. The numerical integration method was incorporated to obtain the POD time coefficients based on the flow equations solved by the conventional finite volume method. Two complex fracture cases reflecting high‐contrast porous media in a two‐dimensional domain were designed to verify the accuracy and efficiency of the established Galerkin‐free POD‐ROM. Sensitivity analysis of parameters was conducted to examine the adaptability of the ROM. The results illustrate that, compared with the fine‐scale model, the ROM can significantly reduce the CPU time without compromising the quality of the numerical solutions.
机译:使用传统的高保真数值模拟来模拟真实田间在裂缝多孔介质中的流体流动仍然具有挑战性。当解决矩阵和骨折方程时,它涉及大量的自由度。为了解决这一挑战,我们提出了一种基于适当的正交分解(POD)来构建一个Galerkin的框架来构建阶数模型(ROM)。与先前研究中常用的基于典型的荚基础建模过程相比,可以构建POD-ROM而不会在不执行流程方程的Galerkin投影到由POD基函数跨越的低维空间。结合了数值积分方法,以基于传统有限体积方法解决的流量方程获得POD时间系数。反映在二维结构域中高对比多孔介质的两个复杂骨折案件旨在验证建立的无持久性POD-ROM的准确性和效率。进行了参数的敏感性分析,以检查ROM的适应性。结果说明,与微尺度模型相比,ROM可以显着降低CPU时间而不会影响数值解决方案的质量。

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