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

✍ Scribed by Yan Ding; Mutsuto Kawahara

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 594 KB
• Volume: 27
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/(sici)1097-0363(199801)27:1/4<139::aid-fld655>3.0.co;2-d

✦ Synopsis

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 ¯ow is undertaken. By means of the ®nite element method the two-dimensional base ¯ow 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 ®nite 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 ¯ow is examined. Taylor±Go Èertler-like vortices in the cavity are obtained by means of reconstruction of three-dimensional ¯ows.