MATLAB Code for 3D Steady Micropolar Couette Flow: Numerical Solver with Verification and Parametric Study

This dataset provides a complete, self-contained MATLAB implementation for simulating three-dimensional steady micropolar Couette flow between parallel plates. The code solves the full nonlinear system of micropolar fluid equations—including conservation of linear momentum, angular momentum, and incompressibility—using a semi-implicit finite-difference scheme with upwind convection treatment and pressure correction via a Poisson solver. The model incorporates realistic boundary conditions: the upper plate moves with constant velocity while all other walls are stationary and no-slip. The package includes two main components: (1) a class-based solver (MicropolarCouette3D) that handles grid setup, time-stepping, boundary conditions, and physical property definitions; and (2) a driver script that performs numerical verification against the Newtonian limit (N=0) and conducts a detailed parametric study of the micropolarity parameter N, microstructure length scale m, and Reynolds number Re. Key outputs include velocity profiles, microrotation fields, energy dissipation distributions, convergence histories, and integral dissipation metrics. The analysis demonstrates how micropolar effects alter flow structure, enhance local rotation, and increase total energy dissipation compared to classical fluids. All visualizations are static, high-quality, and suitable for publication. This code is intended for researchers in theoretical and computational fluid dynamics, particularly those studying complex fluids with microstructure (e.g., liquid crystals, ferrofluids, blood analogs). It emphasizes physical fidelity, numerical robustness, and reproducibility—without analytical simplifications.