Lid-Driven Cavity Flow Solver in C++

A modern C++17 implementation of the classical 2D incompressible lid-driven cavity flow benchmark using the Finite Difference Method (FDM) and the Pressure Projection Method.

This project was developed after completing the CFDPython – 12 Steps to Navier–Stokes course as a way of translating the numerical algorithms into a modular C++ codebase while following modern software engineering practices. The repository serves as a foundation for future high-performance CFD implementations using OpenMP, MPI, CUDA, and more advanced numerical methods.

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Solver Overview

The lid-driven cavity problem is one of the most widely used benchmark problems in Computational Fluid Dynamics (CFD). A square cavity is filled with incompressible fluid where the top wall moves at a constant velocity while the remaining walls remain stationary. The resulting recirculating flow provides an excellent validation case for incompressible Navier–Stokes solvers.

Current implementation includes:

• ✅ C++17 implementation
• ✅ Finite Difference Method (FDM)
• ✅ Incompressible Navier–Stokes Equations
• ✅ Pressure Projection Method
• ✅ Gauss-Seidel Pressure Poisson Solver
• ✅ Structured Cartesian Grid
• ✅ Explicit Time Integration
• ✅ No-slip Wall Boundary Conditions
• ✅ Adaptive Time Step Calculation
• ✅ CSV Output
• ✅ Python Visualization Scripts
• ✅ Automated Verification Scripts
• ✅ Ghia et al. (1982) Validation

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Numerical Algorithm

For each iteration the solver performs

1. Compute intermediate velocities
2. Assemble the Pressure Poisson Equation
3. Solve pressure using Gauss-Seidel iteration
4. Remove mean pressure to eliminate pressure null-space drift
5. Correct the velocity field
6. Apply boundary conditions
7. Compute residuals
8. Repeat until convergence

A detailed explanation is provided in docs/METHODOLOGY.md.

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Results

Velocity Magnitude

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Streamlines

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Pressure Contours

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Residual History

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Validation

The numerical solution is validated against the classical benchmark

Ghia, Ghia & Shin (1982)

using

• Horizontal velocity along the vertical centreline
• Vertical velocity along the horizontal centreline

Ghia Validation

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Automated Verification

The repository includes Python scripts for automatic verification of

• Boundary conditions
• Continuity (divergence)
• Residual history
• Pressure contours
• Velocity magnitude
• Streamlines
• Ghia benchmark comparison

Run all scripts

for file in scripts/*.py; do
    python "$file"
done

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Repository Structure

lid-driven-cavity-cpp/
│
├── plots/
│   ├── velocity_plot.png
│   ├── streamline_plot.png
│   ├── pressure_plot.png
│   ├── residual_plot.png
│   └── ghia_validation.png
│
├── docs/
│   └── METHODOLOGY.md
│
├── results/
│   ├── velocity_u.csv
│   ├── velocity_v.csv
│   ├── pressure.csv
│   ├── velocity_magnitude.csv
|   ├── simulation_info.txt
│   ├── x.csv
│   ├── y.csv
│   └── residual_history.csv
│
├── scripts/
│   ├── compare_ghia.py
│   ├── plot_pressure.py
│   ├── common.py
│   ├── plot_velocity.py
│   ├── plot_streamlines.py
│   ├── plot_residual.py
│   ├── verify_bc.py
│   └── check_divergence.py
│
├── src/
│   ├── csv_writer.cpp
│   ├── csv_writer.h
│   ├── main.cpp
│   ├── matrix.h
│   ├── simulation.cpp
│   └── simulation.h
│
├── CMakeLists.txt
├── README.md
└── LICENSE

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Building

Clone the repository

git clone https://github.com/YOUR_USERNAME/lid-driven-cavity-cpp.git

cd lid-driven-cavity-cpp

Build

mkdir -p build
cd build

cmake ..
make -j

cd ..

Run

./LidDrivenCavity

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Requirements

Solver

• C++17
• CMake

Python

• Python 3
• NumPy
• Matplotlib

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Future Improvements

• Higher-order convection schemes
• Successive Over-Relaxation (SOR)
• Multigrid pressure solver
• Staggered grid formulation
• Adaptive mesh refinement
• OpenMP parallelization
• MPI implementation
• CUDA implementation
• VTK output for ParaView
• Multiple Reynolds number validation
• Grid independence studies
• Performance benchmarking

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References

1. Lorena A. Barba et al.

   CFDPython: 12 Steps to Navier–Stokes

2. Ghia, U., Ghia, K. N., & Shin, C. T.

   High-Re solutions for incompressible flow using the Navier–Stokes equations and a multigrid method.

   Journal of Computational Physics, 48(3), 387–411.

3. Ferziger, J. H., & Perić, M.

   Computational Methods for Fluid Dynamics.

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Acknowledgements

This project was inspired by the CFDPython – 12 Steps to Navier–Stokes educational course developed by Professor Lorena A. Barba and collaborators.

While the numerical formulation follows the concepts introduced in that course, the C++ implementation, software architecture, validation workflow, visualization tools, documentation, and future development roadmap were independently designed and implemented as part of my Computational Fluid Dynamics learning journey.

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License

Released under the MIT License.