MATLAB code for automated construction of exact solutions for non-uniform unidirectional flows of a viscous incompressible fluid between permeable plates

This dataset contains a complete MATLAB implementation for the analytical and numerical study of steady viscous incompressible flow between two permeable parallel plates with linearly non-uniform boundary conditions. The code computes the exact analytical solution for the velocity field and derives key hydrodynamic quantities: vorticity, shear stress, pressure distribution, local Reynolds number, and volumetric flow rate. The package generates publication-ready visualizations, including 3D surfaces, contour plots, vector fields, streamlines, and cross-sectional profiles. The solution accounts for wall permeability through the convective term in the Navier–Stokes equation and correctly reduces to the generalized Couette flow in the limit of zero permeability. All results are fully reproducible with the provided code and default parameters.本数据集包含完整的MATLAB实现代码，用于开展两块渗透性平行平板间带有线性非均匀边界条件的定常粘性不可压缩流动的解析与数值研究。该代码可求解速度场的精确解析解，并推导得到涡量、切应力、压力分布、局部雷诺数与体积流量等关键流体力学参数。该工具包可生成符合学术出版标准的可视化图像，涵盖三维曲面图、等值线图、矢量场图、流线图以及截面轮廓图。本解析方案通过纳维-斯托克斯方程（Navier–Stokes equation）中的对流项纳入壁面渗透性的影响，且在壁面渗透性趋近于零的极限条件下，可准确退化为广义库埃特流动（generalized Couette flow）。依托所提供的代码与默认参数，所有计算结果均可完全复现。