Numerical Solution of Steady Incompressible Flow in a Lid-Driven Cavity Using Alternating Direction Implicit Method

Abstract

The study of viscous flow in a lid-driven cavity is carried out using alternating direction implicit method. The conservation form of incompressible Navier–Stokes equation in stream function–vorticity form is solved using second-order accurate central difference scheme in a uniform finite-difference grid mesh. The numerical solution is obtained up to highest Reynolds number 32,500 from the lowest 0.00001 using the grid sizes 129 × 129, 257 × 257 and 513 × 513. Good agreement of the result is found with Erturk et al. (Int J Numer Methods Fluids 48:747–774, 2005) [1]. The study of flow properties in the form of velocity profiles, stream function and vorticity contour plots and location of primary and secondary eddies are carried out. The novelty of this study is that the magnitude of the vorticity value does not cross the theoretical limit −1.8859 (Burggraf 24:113–151, 1966 [2]).