The investigation on SIMPLE and SIMPLER algorithm through lid driven cavity

The present study analyzes in details to compare SIMPLE and SIMPLER algorithm in terms of their convergence rate, iteration number and computational time. The work which is based on primitive variables (u, v, P) formulation of Navier-Stokes equations to investigate the velocity and pressure distribution in the square cavity at Reynolds number of 100 and 400. The solutions are obtained for grid size 16 × 16 up to 256 × 256. From the plots of velocity profiles along centerline geometry, it shows good agreement with the benchmark solution from past researchers. The velocity and pressure in the cavity varies as the Reynolds number increases from 100 to 400. SIMPLER algorithm is proven to be more efficient compared to SIMPLE as iteration number required for a given Reynolds number and grid size is lower than that of SIMPLE. The values of under-relaxation factors for velocity components and pressure play significant role in terms of convergence rate of a numerical scheme.