Basic CFD Flows in Python

Two classic CFD problems implemented with finite differences for learning flow physics and numerical methods.

This project features two classic incompressible CFD flow problems implemented from scratch in Python using finite difference methods. These examples serve as a foundation for learning numerical methods, simulation workflow, and understanding basic flow physics.

Included Problems

1. Lid-Driven Cavity Flow

  • Solves the incompressible Navier–Stokes equations in a 2D square domain.
  • The top wall (lid) moves with constant velocity, generating vortices in the cavity.
  • Implements a pressure Poisson equation using:
    • Dirichlet conditions on pressure
    • Neumann conditions for velocity walls
  • Uses:
    • Fixed uniform grid (default: 100×100)

    • Explicit time-stepping scheme

2. Channel Flow

  • Simulates pressure-driven flow between two parallel horizontal plates
  • Periodic boundary conditions in the streamwise direction
  • Solves the incompressible Navier–Stokes equations using finite differences
  • Includes:
    • Iterative pressure-velocity solver

Results and Discussion

Lid-Driven Cavity Flow

Velocity vectors showing the main vortex structure
Streamline plot visualizing circulation inside the cavity

Observations:

  • A strong primary vortex forms in the center, driven by the top lid.
  • Secondary eddies begin to form near the corners as time advances.
  • The flow stabilizes after sufficient time steps, showing smooth velocity distribution.

Channel Flow

Streamwise velocity vectors inside the channel
velocity distribution
Boundary layers and shear zones visualized via vorticity
u vs y profile confirming parabolic trend

Observations:

  • Smoothed velocity field shows clean profile across the channel.
  • Vorticity plot highlights boundary-layer effects near walls.
  • Centerline velocity matches parabolic-like behavior, confirming solver accuracy.

Conclusion

These simulations demonstrate fundamental fluid dynamics behaviors using classical numerical methods. Both cases validate the accuracy of solving the incompressible Navier–Stokes equations using finite difference schemes, with meaningful post-processing for analysis and interpretation.

🔗 View Project on GitHub