We present numerical simulations of post-Darcy flow in thin porous medium: one consisting of staggered arrangements of circular cylinders and one random distribution of cylinders bounded between walls. The simulations span a range of Reynolds numbers, 40 to 4000, where the pressure drop varies nonlinearly with the average velocity, covering nonlinear laminar flow to the fully turbulent regime. The results are compared to those obtained by replacing the bounding walls with symmetric boundaries with the aim to reveal the effect of bounding walls on microscopic characteristics and macroscopic measures, i.e., pressure drop, hydrodynamic dispersion and Reynolds stresses. We use large eddy simulation to directly calculate the Reynolds stresses and turbulent intensity. The simulations show that vortical structures emerge at the boundary between the cylinders and the bounding walls causing a difference between the microscopic flow in the confined and non-confined porous media. This affects the averaged values of pressure drop, the hydrodynamic dispersion and the Reynolds stresses. Finally, the distance between the bounding walls is altered with the particle Reynolds number kept constant. It is observed that the difference between results calculated in confined and non-confined cases increases when the bounding walls are narrower.

我们提供了达西后稀薄多孔介质中流动的数值模拟：一种由交错排列的圆柱体组成，另一种是随机分布在壁之间的圆柱体。该模拟跨越雷诺数范围（40到4000），其中压降随平均速度非线性变化，涵盖了到完全湍流状态的非线性层流。将结果与通过用对称边界替换边界壁而获得的结果进行比较，目的是揭示边界壁对微观特性和宏观测量（即压降，流体动力分散和雷诺应力）的影响。我们使用大型涡模拟直接计算雷诺应力和湍流强度。模拟表明，在圆柱体与边界壁之间的边界处出现了涡旋结构，从而在受限和非受限的多孔介质中产生了微观流动差异。这会影响压降，流体动力分散和雷诺应力的平均值。最后，在雷诺数保持不变的情况下改变边界壁之间的距离。可以观察到，当边界壁更窄时，在受限和非受限情况下计算的结果之间的差异会增加。边界壁之间的距离随雷诺数保持恒定而改变。可以观察到，当边界壁更窄时，在受限和非受限情况下计算的结果之间的差异会增加。边界壁之间的距离随雷诺数保持恒定而改变。可以观察到，当边界壁更窄时，在受限和非受限情况下计算的结果之间的差异会增加。