naca-cfd-solver

A two-dimensional cell-centred finite-volume CFD solver written from scratch in C++17, carried from analytical verification and a lid-driven cavity benchmark through to wall-resolved k-omega SST simulations of a NACA 0012 at a chord Reynolds number of 6×10⁶.

Nothing here is delegated to a CFD package. Geometry, mesh generation, the finite-volume discretisation, the SIMPLE pressure-velocity coupling, the non-orthogonal correction and the turbulence model are all implemented in this repository. There is no external numerical library either: the linear systems are solved by a Gauss-Seidel sweep with over-relaxation written for this project. The only third-party code involved is NumPy and Matplotlib, used for plotting after the fact.

Velocity magnitude around the NACA 0012 at 10° incidence and Re = 6×10⁶, from the k-omega SST solver with limited second-order convection.

Results

Check	Result
Laplace on an annulus, against the analytical solution	2nd order, observed 1.98 → 2.00
Convection-diffusion, central differencing	2nd order, observed 2.02 → 2.00
Convection-diffusion, first-order upwind	1st order, observed 0.73 → 0.95
Lid-driven cavity at Re = 100, against Ghia et al. (1982)	centreline profiles matched
Lift at zero incidence, where the exact answer is zero	Cl = 2.3×10⁻⁷
Lift at 10° against the NASA three-code SST mean of 1.079	Cl = 1.119, 3.6 % high
Near-wall resolution in the final solution	mean y⁺ = 1.07, no wall functions

Reference data comes from Ghia, Ghia and Shin (1982) for the cavity, and from the NASA Turbulence Modeling Resource for the turbulent aerofoil.

How it is organised

Every program is a self-contained translation unit with its own main(). They communicate through CSV files on disk rather than through a shared library, which is what allows any stage to be re-run without rebuilding the ones before it. The layout follows the order the project was actually built in.

src/
├── verification/   analytical cases, solved before anything was trusted
│   ├── laplace_annulus_verification.cpp        Laplace on an annulus
│   └── convection_diffusion_verification.cpp   central vs first-order upwind
├── cavity/         lid-driven cavity, built up in stages
│   ├── lid_driven_cavity_stage2_u_predictor.cpp   momentum predictor alone
│   └── lid_driven_cavity_final.cpp                full SIMPLE loop, Re = 100
├── mesh/           geometry and structured O-grid generation
│   ├── naca_geometry.cpp                       NACA 4-digit surface coordinates
│   ├── naca_fvm_geometry.cpp                   cell metrics, areas, normals
│   ├── laplace_naca_v1.cpp                     first O-grid, elliptic smoothing
│   ├── generate_highRe_mesh.cpp                rebuilt O-grid for y⁺ ≈ 1
│   └── generate_grid_convergence_meshes.cpp    coarse, medium and fine meshes
└── solver/         the aerofoil solver
    ├── naca_flow_setup.cpp            fields, boundary conditions, initialisation
    ├── naca_momentum_predictor.cpp    momentum predictor on the aerofoil mesh
    ├── naca_simple_orthogonal.cpp     SIMPLE, orthogonal fluxes only
    ├── naca_simple_nonorth.cpp        with the non-orthogonal correction
    ├── naca_sst.cpp                   k-omega SST, first-order convection
    ├── naca_sst_alpha0.cpp            the same at 0°, as a symmetry check
    └── naca_sst_second_order.cpp      limited second-order convection, final

python/ holds the post-processing and the convergence analysis, data/ the small reference results the figures are drawn from, and scripts/ the PowerShell driver used for the grid-convergence sweep. The multi-megabyte field files each run produces are not tracked.

Build

Requires a C++17 compiler, CMake 3.20 or newer, and Ninja. On Windows this was built with MinGW-w64 UCRT64 from MSYS2.

cmake -S . -B build -G Ninja
cmake --build build

That produces one executable per program in build\. On MinGW they are linked statically, so they carry their own runtime and will start on a machine with no MSYS2 installation and nothing added to PATH.

Run

Each program writes its CSV output to the current working directory, so run them from output\ to keep results out of the source tree. The two analytical verification cases take about a minute each and need no input:

cd output
..\build\laplace_annulus_verification.exe
..\build\convection_diffusion_verification.exe

The aerofoil cases read the mesh written by the mesh generator, so those run in order:

..\build\generate_highRe_mesh.exe
..\build\naca_sst_second_order.exe

The turbulent aerofoil runs take hours. The cavity and verification cases are the quick way to see the numerics working.

Post-processing

python -m pip install numpy scipy pandas matplotlib
python ..\python\plot_naca_sst.py