This article addresses the problem of choosing the optimal discretization grid for emulating fluid flow through a pipeline. The aggregated basic flow model is linearized near the operating point obtained from the steady state analytic solution of the differential equations under consideration. Based on this model, the relationship between the Courant number (μ) and the stability margin is examined. The numerically set coefficient ${\mu }_{opt}$, ensuring the maximum margin of stability, is analyzed in terms of the physical and technological parameters of the flow. As a result of this analysis, a specific formula is obtained based on parameters describing the mechanics (geometry and physics) of the flow through the pipeline, which leads to the optimal value of the Courant number, separately for smooth and rough pumping conditions. A more detailed analysis of the distribution of the optimal μ coefficient in relation to the parameters of the pipeline flow mechanics shows four cases to consider when determining the coefficient ${\mu }_{opt}$. Surprisingly, in three cases, the CFL condition is insufficient, which is expressed in the form of the proposed procedure for choosing the optimal value of μ. The final dichotomous model is derived from the Monte Carlo simulation results in which the effect of each parameter on the optimal Courant number is estimated and consolidated. Taking into account the recognized general laws of physics and using numerical methods and mathematical analysis, simple and useful analytical relationships describing the flow process are obtained. In addition, computer simulations are performed to verify the correctness of the proposed procedure, as well as a number of other considerations related to the modeling of fluid flow in transport pipelines.

本文解决了选择最佳离散网格以模拟通过管道的流体流动的问题。汇总的基本流量模型在工作点附近线性化，该工作点是根据所考虑的微分方程的稳态解析解得出的。基于此模型，研究了库仑数（μ）与稳定裕度之间的关系。数值设定系数${\mu }_{ØpŤ}$根据流量的物理和技术参数来分析确保最大稳定性的流量。分析的结果是，根据描述流过管道的力学（几何和物理）的参数，获得了一个特定的公式，从而分别得出了平滑和粗糙抽运条件下的库兰特数的最佳值。有关最佳μ系数与管道流动力学参数相关的分布的更详细分析显示，在确定系数时要考虑的四种情况${\mu }_{ØpŤ}$。出乎意料的是，在三种情况下，CFL条件不足，以建议的选择μ最佳值的过程的形式表示。最终的二分模型是从Monte Carlo模拟结果得出的，在该结果中，每个参数对最佳Courant数的影响都得到了估计和合并。考虑到公认的一般物理定律，并使用数值方法和数学分析，可获得描述流动过程的简单有用的分析关系。另外，执行计算机仿真以验证所提出程序的正确性，以及与运输管道中流体流动建模有关的许多其他考虑因素。