Multiscale Method for Oseen Problem in Porous Media with Non-periodic Grain Patterns
Multiscale Method for Oseen Problem in Porous Media with Non-periodic Grain Patterns
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DOI：
10.1007/s11242-016-0762-3
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发表时间：
2016-05
影响因子：
2.7
通讯作者：
B. Muljadi
中科院分区：
文献类型：
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作者：
B. Muljadi
准确预测描述多孔介质流动所需的宏观流动参数依赖于对更小尺度（孔隙空间）流场分布的良好了解。孔隙空间的惯性效应不可低估，但在大规模流体流动模拟中往往被忽略。我们提出了一种多尺度方法来求解Oseen近似的非周期性颗粒结构中孔隙空间的不可压缩流动。该方法以多尺度有限元法为基础[MsFEM Hou and Wu in J computer Phys 134:169-189, 1997]，建立在Crouzeix和Raviart单元的基础上（Crouzeix和Raviart in Math Model num Anal 7:33-75, 1973）。对高度非周期条件下的惯性流动进行了模拟。给出了相对于参考解的数值误差方面的收敛性研究，以证明我们的方法的准确性。在粗糙单元边缘上的弱强制连续性被证明可以在晶粒附近保持精确的解，而不需要任何过采样方法。采用惩罚方法，可以使用简单的笛卡尔网格对复杂的颗粒模式进行建模。这项工作是解决具有非线性惯性项的更复杂的Navier-Stokes方程的垫脚石。
Accurate prediction of the macroscopic flow parameters needed to describe flow in porous media relies on a good knowledge of flow field distribution at a much smaller scale—in the pore spaces. The extent of the inertial effect in the pore spaces cannot be underestimated yet is often ignored in large-scale simulations of fluid flow. We present a multiscale method for solving Oseen’s approximation of incompressible flow in the pore spaces amid non-periodic grain patterns. The method is based on the multiscale finite element method [MsFEM Hou and Wu in J Comput Phys 134:169–189, 1997)] and is built in the vein of Crouzeix and Raviart elements (Crouzeix and Raviart in Math Model Numer Anal 7:33–75, 1973). Simulations of inertial flow in highly non-periodic settings are conducted and presented. Convergence studies in terms of numerical errors relative to the reference solution are given to demonstrate the accuracy of our method. The weakly enforced continuity across coarse element edges is shown to maintain accurate solutions in the vicinity of the grains without the need for any oversampling methods. The penalisation method is employed to allow a complicated grain pattern to be modelled using a simple Cartesian mesh. This work is a stepping stone towards solving the more complicated Navier–Stokes equations with a nonlinear inertial term.