MATLAB Implementation of Analytical Solution with Optimal Truncation for Unsteady Couette Flow with Permeable Walls
Description
This MATLAB code computes the exact analytical solution for unsteady Couette flow of a viscous incompressible fluid between two parallel permeable plates, where the velocity field includes a linear shear component. The solution is expressed as a Fourier series with analytically derived coefficients, and the code automatically determines the optimal number of terms required to achieve a user-specified accuracy (default: 1e-4). The package includes numerical validation against a finite-difference solver, comprehensive visualization tools (2D/3D plots, vector fields, convergence curves), and a ready-to-use function solve_Couette_flow.m for external applications. This implementation provides a reliable benchmark for verifying numerical methods in fluid dynamics and for studying the effects of wall permeability on transient flow behavior.
Files
Steps to reproduce
Requirements: MATLAB R2020b or later (base MATLAB only; no additional toolboxes required) Steps: 1. Download the file Couette_flow_analysis.m 2. Execute the script in MATLAB 3. The code will automatically: Compute analytical solutions using Fourier series expansion Generate 9 figures showing velocity profiles, convergence analysis, parameter studies, and numerical validation Save the standalone function solve_Couette_flow.m to the current directory Customization: To use the solver independently, call: [U, u1, Vx] = solve_Couette_flow(z, t, y, W, Omega, w, nu, N) The number of series terms N is optional and will be automatically optimized if omitted. Output: All plots appear in separate windows with SI units and Times New Roman font. Relative errors from numerical validation are printed to the command window. Expected runtime: 30–60 seconds on a standard computer.
Institutions
- Samara State Technical University
- Ural'skij federal'nyj universitet imeni pervogo Prezidenta Rossii B N El'cina