Application of an ADI scheme for steady and periodic solutions in a lid‐driven cavity problem

Abstract

Purpose

The purpose of the paper is to study the steady and periodic solution of a lid‐driven cavity flow problem with the gradual increase of Reynolds number (Re) up to 10,000.

Design/methodology/approach

The problem is solved by unsteady stream function‐vorticity formulation using the clustered grids. The alternating direction implicit (ADI) method and the central difference scheme have been used for discretization of the governing equations. Total vorticity error and the total kinetic energy have been considered for ensuring the state of flow condition. The midplane velocity distribution and the top wall vortex distribution are compared with the results of other authors and found to show good agreement.

Findings

Kinetic energy variation with time is studied for large time computation. Below 7,500, it becomes constant signifying the flow to be in steady‐state. At Re=10,000, the fluid flow has an oscillating nature. The dimensionless period of oscillation is found to be 1.63. It is demonstrated that the present computation is able to capture the periodic solution after the bifurcation very accurately.

Originality/value

The findings will be useful in conducting a steady and periodic solution of variety of fluid flows or thermally‐driven fluid flows.

Citation

Das, M.K. and Rajesh Kanna, P. (2007), "Application of an ADI scheme for steady and periodic solutions in a lid‐driven cavity problem", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 17 No. 8, pp. 799-822. https://doi.org/10.1108/09615530710825783