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Pores resolving simulation of Darcy flows

机译：达西流的孔隙解析模拟

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摘要

A theoretical formulation and corresponding numerical solutions are presented for microscopic fluid flows in porous media with the domain sufficiently large to reproduce integral Darcy scale effects. Pore space geometry and topology influence flow through media, but the difficulty of observing the configurations of real pore spaces limits understanding of their effects. A rigorous direct numerical simulation (DNS) of percolating flows is a formidable task due to intricacies of internal boundaries of the pore space. Representing the grain size distribution by means of repelling body forces in the equations governing fluid motion greatly simplifies computational efforts. An accurate representation of pore-scale geometry requires that within the solid the repelling forces attenuate flow to stagnation in a short time compared to the characteristic time scale of the pore-scale flow. In the computational model this is achieved by adopting an implicit immersed-boundary method with the attenuation time scale smaller than the time step of an explicit fluid model. A series of numerical simulations of the flow through randomly generated media of different porosities show that computational experiments can be equivalent to physical experiments with the added advantage of nearly complete observability. Besides obtaining macroscopic measures of permeability and tortuosity, numerical experiments can shed light on the effect of the pore space structure on bulk properties of Darcy scale flows.
机译：为多孔介质中的微观流体流动提供了理论公式和相应的数值解，其区域足够大以重现积分的达西尺度效应。孔隙空间的几何形状和拓扑结构会影响流过介质的流动，但是难以观察实际孔隙空间的配置限制了对其影响的理解。由于孔隙空间内部边界的复杂性，对渗流进行严格的直接数值模拟（DNS）是一项艰巨的任务。通过在控制流体运动的方程式中排斥体力来表示晶粒尺寸分布，极大地简化了计算工作。孔尺度几何形状的精确表示要求，与孔尺度流的特征时间尺度相比，排斥力在短时间内使流动衰减至停滞状态。在计算模型中，这是通过采用隐式浸入边界方法实现的，该方法的衰减时间尺度小于显式流体模型的时间步长。对通过随机产生的不同孔隙度的介质进行的流动的一系列数值模拟表明，计算实验可以等同于物理实验，并具有几乎完全可观测的优点。数值实验除了获得渗透率和曲折度的宏观度量外，数值实验还可以揭示孔隙空间结构对达西规模水流体性质的影响。

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