Numerical Solution of the 2D Incompressible Navier–Stokes Equations

Overview

This project solves the 2D incompressible Navier–Stokes equations for the lid-driven cavity benchmark using a fractional step method on a staggered (MAC) grid. Pressure is obtained from a Poisson equation (solved efficiently via DCT). The solver is validated against Ghia et al. (1982) centerline benchmarks.

Highlights

• Staggered (MAC) grid for stable pressure–velocity coupling
• Projection method: predictor → pressure Poisson → velocity correction
• Tests at Re = 400, 1000, 3200
• Validation vs. Ghia et al.

Code

• The code is available on GitHub

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