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Multiscale Hybrid-Mixed Finite Element Method for Flow Simulation in Fractured Porous Media

机译:多尺度混合混合有限元法在裂缝多孔介质中的流动模拟

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The multiscale hybrid-mixed(MHM)method is applied to the numerical approximation of two-dimensional matrix fluid flow in porous media with fractures.The two-dimensional fluid flow in the reservoir and the one-dimensional flow in the discrete fractures are approximated using mixed finite elements.The coupling of the two-dimensional matrix flow with the one-dimensional fracture flow is enforced using the pressure of the one-dimensional flow as a Lagrange multiplier to express the conservation of fluid transfer between the fracture flow and the divergence of the one-dimensional fracture flux.A zero-dimensional pressure(point element)is used to express conservation of mass where fractures intersect.The issuing simulation is then reduced using the MHM method leading to accurate results with a very reduced number of global equations.A general system was developed where fracture geometries and conductivities are specified in an input file and meshes are generated using the public domain mesh generator GMsh.Several test cases illustrate the effectiveness of the proposed approach by comparing the multiscale results with direct simulations.
机译:将多尺度混合(MHM)方法应用于具有裂缝的多孔介质中的二维矩阵流体流动的数值逼近。储存器中的二维流体流动和离散裂缝中的一维流动的近似使用混合有限元。使用一维裂缝流的二维矩阵流的耦合使用一维流动的压力作为拉格朗日乘法器来表达裂缝流动之间的流体转移和偏差的节约一维骨折通量。零尺寸压力(点元素)用于表达骨折相交的质量守恒。然后使用MHM方法减少发布模拟,导致具有非常减少数量的全局方程的准确结果。使用公共域网格生成骨折几何和电导率在输入文件中指定裂缝几何和电导率的常规系统Generator GMSH.Several测试用例通过将多尺度结果与直接仿真进行比较来说明所提出的方法的有效性。

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