Vol.26, Special Issue B, 2026, pp. S61–S71
https://doi.org/10.69644/ivk-2026-siB-0061 

This study presents a numerical investigation of Newtonian two-dimensional lid-driven square cavity fluid flow up to Reynolds numbers of 5000 using a grid size of 501×501. Building on earlier research, the work explores two-sided and four-sided wall-motion scenarios to analyse multiple and unique flow solutions. For the two-sided case, multiple solutions occur when both the left and upper walls move downward and rightward at equal speed, while unique solutions arise when the left wall moves at speed 1.5 and the upper wall at speed 1, with the right and bottom walls fixed. For the four-sided case, multiple solutions are observed when all walls move at equal speed in opposing directions, whereas unique solutions emerge when either the left or bottom wall moves at speed 1.5 while the others move at speed 1. The flow field exhibits symmetry along cavity diagonals, bifurcating to asymmetric patterns at Reynolds numbers of 1466 (two-sided) and 175 (four-sided). Between Reynolds numbers 175 and 385, two stable solutions exist, and beyond 385, three stable solutions are observed for the four-sided equal-speed case. Increasing one wall’s speed to 1.5 transitions the flow from multiple to unique stable solutions. Velocity profiles and streamline contours are analysed to characterise these behaviours. Computations are performed using the PARAM Shavak HPC system.

Keywords: • finite volume technique • lid-driven cavity • boundary value problems • incompressible flow • Navier-Stokes equations • partial differential equations