MATLAB Implementation of Analytical Solution with Optimal Truncation for Unsteady Couette Flow with Permeable Walls

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.