Numerical Study of the 2D Incompressible Navier-Stokes Equations

Mayank K Patel, Mohini Desai

Abstract: The numerical investigation of the two-dimensional incompressible Navier-Stokes equations using the stream function-vorticity formulation and finite-difference methods. A second-order central-difference spatial discretization combined with an explicit time-stepping scheme for vorticity transport and an iterative Poisson solver for the Stream function is implemented. The lid-driven cavity flow is used for validation and results are reported for Reynolds number Re=100, 400, 1000 and 5000. Grid convergence and residual behaviour are analysed. The numerical method demonstrates good agreement with classical benchmark results for velocity profiles and vortex structure and the study discusses stability, accuracy and computational cost considerations.

Keywords: Navier-Stokes, Stream function-vorticity, finite difference, lid-driven cavity, iterative Poisson solver, Reynolds number

How to Cite?: Mayank K Patel, Mohini Desai, "Numerical Study of the 2D Incompressible Navier-Stokes Equations", Volume 14 Issue 12, December 2025, International Journal of Science and Research (IJSR), Pages: 600-608, https://www.ijsr.net/getabstract.php?paperid=SR251208174529, DOI: https://dx.doi.org/10.21275/SR251208174529