Lid-Driven Cavity Flow Solver in MATLAB

A MATLAB implementation of the two-dimensional lid-driven cavity benchmark.

This repository is one part of a larger project where the same CFD benchmark will be implemented and compared in MATLAB, C++, C, Python, OpenMP, MPI, CUDA, and OpenFOAM. The goal is to keep the physical setup the same across all versions, then compare accuracy, runtime, implementation style, and scalability.

This version is the MATLAB reference implementation. It is useful for developing the numerical method, checking the post-processing workflow, and comparing loop-based and vectorized MATLAB code before moving to lower-level and parallel implementations.

What is included

• Structured collocated Cartesian grid
• Pseudo-transient pressure-correction algorithm
• Loop-based and vectorized momentum predictors
• First-order upwind and central convection schemes
• Red-black Gauss-Seidel and red-black SOR pressure solvers
• Validation against Ghia et al. centreline velocity data
• Automated field plots, validation plots, residual histories, and CSV summaries

The full parameter study runs 72 combinations:

3 meshes × 3 Reynolds numbers × 2 schemes × 2 pressure solvers × 2 implementations

Representative result

For all implementations in this benchmark series, I want to keep the result layout the same: flow-field plots on one side and Ghia centreline validation on the other. This makes the MATLAB, C++, and later OpenMP/MPI/CUDA/OpenFOAM versions easier to compare.

This MATLAB case uses N = 64, Re = 100, central differencing, RBGS, and the vectorized momentum predictor.

Flow field	Centreline validation

Numerical approach

The solver advances the non-dimensional incompressible Navier-Stokes equations through pseudo-time. At each outer iteration it predicts the velocity field, solves a pressure-correction Poisson equation, corrects velocity and pressure, reapplies the wall boundary conditions, and records convergence diagnostics.

A more detailed description is available in docs/METHODOLOGY.md.

Study observations

• 44/72 cases met the selected Ghia centreline-error limits.
• All N = 128 cases met the selected validation limits.
• Coarse high-Reynolds-number cases were less accurate, which is expected for this setup.
• RBSOR reduced pressure-solver iterations and runtime compared with RBGS.
• Vectorizing the momentum predictor had a limited effect on total runtime because the pressure solve remained the main cost.

The validation limits are practical comparison thresholds, not a replacement for a formal verification or grid-independence study. See docs/RESULTS.md for the full discussion.

Run the project

Clone the repository, open MATLAB in the repository root, and run one of:

main_quick    % reduced check
main_medium   % study without the N = 128 mesh
main          % full 72-case study

Linux shell wrappers are also available:

bash scripts/run_quick.sh
bash scripts/run_medium.sh
bash scripts/run.sh

Generated files are written to results/data/ and results/figures/. Detailed instructions are in docs/RUNNING.md.

Repository layout

config/        default solver and study settings
startup/       path setup and output-folder creation
core/          solver routines
studies/       single-case and parameter-study runners
validation/    Ghia data and error calculations
post/          plotting and result export
scripts/       shell wrappers for MATLAB runs
assets/        selected figures and published summary data
docs/          methodology, results, validation, and running notes
results/       generated output; ignored by Git

Requirements

This project uses base MATLAB scripts and functions.

No external MATLAB toolboxes are required for the main solver workflow.

Limitations

This is an educational solver, not a replacement for a production CFD package. It uses a collocated grid without Rhie-Chow interpolation and an iterative pressure solver without multigrid acceleration. The convergence strategy and pressure-velocity treatment are the main areas for further improvement.

Next steps

• Improve convergence control and stopping criteria
• Improve the high-Reynolds-number cases
• Use this MATLAB version as the reference case while adding the C++, C, Python, OpenMP, MPI, CUDA, and OpenFOAM versions
• Keep the result layout consistent across all implementations
• Build one comparison table for accuracy, runtime, and speedup across the full benchmark suite

Reference

Ghia, U., Ghia, K. N., & Shin, C. T. (1982). High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. Journal of Computational Physics, 48(3), 387-411.

Author

Ahmed Kandil — Portfolio · LinkedIn

Released under the MIT License.