Numerical Solutions of 2-D Steady Incompressible Driven Cavity Flow at High Reynolds Numbers

TL;DR

This paper presents high-resolution numerical solutions for 2-D steady incompressible driven cavity flow at high Reynolds numbers, revealing new vortex structures and validating results against benchmarks.

Contribution

It introduces a highly accurate numerical approach using a 601x601 grid to solve Navier-Stokes equations at high Reynolds numbers, discovering new vortex phenomena.

Findings

Identification of a new quaternary vortex at the bottom left corner.

Discovery of a tertiary vortex at the top left corner.

Numerical solutions achieved with residuals less than 10^-10.

Abstract

Numerical calculations of the 2-D steady incompressible driven cavity flow are presented. The Navier-Stokes equations in streamfunction and vorticity formulation are solved numerically using a fine uniform grid mesh of 601x601. The steady driven cavity solutions are computed for Re<21,000 with a maximum absolute residuals of the governing equations that were less than 10-10. A new quaternary vortex at the bottom left corner and a new tertiary vortex at the top left corner of the cavity are observed in the flow field as the Reynolds number increases. Detailed results are presented and comparisons are made with benchmark solutions found in the literature.