MATLAB code for automated construction of exact solutions for non-uniform unidirectional flows of a viscous incompressible fluid between permeable plates
Description
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.
Files
Steps to reproduce
To reproduce the results in this dataset, follow these steps: 1. Download all files from this dataset, including the main script `flow_permeable_couette.m` and the `README.txt` file. 2. Open MATLAB (version R2023b or later is recommended). 3. Set the MATLAB current folder to the directory containing the downloaded files. 4. Run the script by typing in the Command Window: >> flow_permeable_couette 5. The code will automatically: - Compute the analytical solution for the base case (W0 = -0.005 m/s, W1 = 0.005 m/s, w = 0.01 m/s); - Generate 10 publication-ready figures (3D surface, contour/vector plots, streamlines, cross-sectional profiles, and a flow rate map Q(W0, W1)); - Output the volumetric flow rate and global Reynolds number to the Command Window. 6. To explore other cases, modify the parameters `W0_base`, `W1_base`, `Omega0`, `Omega1`, or `w_base` in the script and re-run. 7. No external toolboxes are required — only built-in MATLAB functions are used. Results are fully deterministic and reproducible across systems.
Institutions
- Samara State Technical University
- Ural'skij federal'nyj universitet imeni pervogo Prezidenta Rossii B N El'cina