Linear stability of incompressible fluid flow in a cavity using finite element method

Numerical methods have been applied to theoretical studies of instability and transition to turbulence. In this study an analysis of the linear stability of incompressible flow is undertaken. By means of the finite element method the two-dimensional base flow is computed numerically over a range of Reynolds numbers and is perturbed with three-dimensional disturbances. The partial differential equations governing the evolution of perturbation are obtained from the non-linear Navier–Stokes equations with a slight compressibility by using linear stability and normal mode analysis. In terms of the finite element discretization a non-singular generalized eigenproblem is formulated from these equations whose solution gives the dispersion relation between complex growth rate and wave number. This study presents stability curves to identify the critical Reynolds number and critical wavelength of the neutral mode and discusses the mechanism of instability. The stability of lid-driven cavity flow is examined. Taylor–Goertler-like vortices in the cavity are obtained by means of reconstruction of three-dimensional flows. © 1998 John Wiley & Sons, Ltd.

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