Another Look at the Driven Cavity Problem

Numerical analysis of a lid driven cavity is a standard computational fluid dynamics problem. A semi-discrete method known as the method of lines is used in this report to reduce the problem to one of solving a coupled system of first-order linear differential equations and linear algebraic equations. The spectrum of the coefficient matrix in the first-order system of differential equations is analyzed as the flow field evolves from rest to steady state. By examining the pattern of this eigenvalue migration it is possible to estimate the time to steady state by using very coarse grids. A simple relationship between the Reynolds number and time to steady state is also apparent from analyzing the coefficient matrix... Computational fluid dynamics, Spectral analysis, Driven cavity problem, Method of lines.