标题： 使用计算机代数推导薄膜平均方程 显示英文标题

标题： Deriving thin-film averaged equations using computer algebra

摘要： 我们展示了使用计算机代数来促进薄膜降阶模型推导的用途。 我们专注于加权残差积分边界层（WRIBL）方法，该方法已被证明是通过在薄间隙方向上对纳维-斯托克斯方程进行平均而开发降阶模型的一种非常有效的方法。 特别是，我们使用SymPy（Python中的符号计算库）来推导Dietze和Ruyer-Quil（J. Fluid Mech. 762, 60, 2015）的环状核心WRIBL模型；由于包含二阶项、存在两个水动力活跃相、施加界面边界条件以及圆柱几何结构，该推导尤其复杂。 我们使用代码摘录来展示如何将推导的每一步分解为适合符号计算的子步骤。 为了说明所推导模型的应用，我们使用Python中的科学计算库对其进行数值求解，并简要探讨瑞利-普拉托不稳定性动力学。 以此处描述的方式使用开源计算机代数，大大简化了平均模型的推导，从而促进了其在多尺度流动研究以及计算高效预测和优化中的应用。 显示英文摘要

摘要： We demonstrate the use of computer algebra for facilitating the derivation of thin film reduced-order models. We focus on the weighted residual integral boundary layer (WRIBL) method, which has proven to be a very effective technique for developing reduced-order models by averaging the Navier-Stokes equations over the thin-gap direction. In particular, we use SymPy (the symbolic computing library in Python) to derive the core-annular WRIBL model of Dietze and Ruyer-Quil (J. Fluid Mech. 762, 60, 2015); the derivation is especially involved due to the inclusion of second-order terms, the presence of two hydrodynamically active phases, the enforcement of interfacial boundary conditions, and the cylindrical geometry. We show, using excerpts of code, how each step of the derivation can be broken down into substeps that are amenable to symbolic computation. To illustrate the application of the derived model, we solve it numerically using scientific computing libraries in Python, and briefly explore the dynamics of the Rayleigh-Plateau instability. The use of open-source computer algebra, in the manner described here, greatly eases the derivation of averaged models, thereby facilitating their use for the study of multiscale flows, as well as for computationally-efficient prediction and optimization.