Dept. Física Fundamental, Universidad Nacional de Educación a Distancia, Aptdo. 60141 E-28080, Madrid, Spain.
Facultad de Ingeniería y Arquitectura, Universidad Pontificia Bolivariana, Montería 230002, Colombia.
Phys Rev E. 2019 Dec;100(6-1):062133. doi: 10.1103/PhysRevE.100.062133.
A simple Markovian theory for the prediction of averages and correlations of discrete hydrodynamics near parallel solid walls is presented. The discrete momentum of bins is defined through a finite element basis function. The effect of the walls on the fluid is through irreversible extended friction forces appearing in the very equations of hydrodynamics. The Markovian assumption is critically assessed from the exponential decay of the eigenvalues of the correlation matrix of the discrete transverse momentum. We observe that for bins smaller than molecular dimensions, allowing one to resolve the density layering near the wall, the dynamics near the wall is non-Markovian. Bins larger than the molecular size do behave in a Markovian way. We measure the nonlocal viscosity and frictions kernels that appear in the discrete hydrodynamic equations, which are given in terms of Green-Kubo formulas. They suffer dramatically from the plateau problem. We use a recent procedure for reliably extracting the transport kernels out of the plateau-problematic Green-Kubo formula. With the so-measured transport kernels the nonlocal theory predicts very well the decay of the average of the transverse momentum when the initial velocity profile is a plug flow. The theory allows us to derive the slip boundary condition with microscopic expressions for the slip length and the hydrodynamic position of the wall. The slip boundary condition is not satisfied at the initial stages of the discontinous plug flow, but good agreement is obtained at later stages.
本文提出了一种简单的马尔可夫理论，用于预测平行固壁附近离散流体动力学的平均值和相关性。通过有限元基函数定义了箱的离散动量。壁面对流体的影响是通过不可逆的扩展摩擦力出现在流体动力学的方程中。从离散横向动量相关矩阵的特征值的指数衰减来看，我们批判性地评估了马尔可夫假设。我们观察到，对于比分子尺寸小的箱子，允许解析壁附近的密度分层，壁附近的动力学是非马尔可夫的。比分子尺寸大的箱子以马尔可夫的方式表现。我们测量了出现在离散流体动力学方程中的非局部粘度和摩擦核，这些核是根据格林-库珀公式给出的。它们受到平台问题的严重影响。我们使用一种最近的程序，从有平台问题的格林-库珀公式中可靠地提取出输运核。用所测量的输运核，非局部理论很好地预测了横向动量平均值的衰减，当初始速度分布为塞流时。该理论允许我们从微观表达式导出滑移边界条件，包括滑移长度和壁的流体力学位置。在间断塞流的初始阶段，滑移边界条件不满足，但在后期阶段得到了很好的一致性。
