Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

Solenoidal invariance of the dynamics for stability calculations

J.I.H. Lópeza,*, J.R. Meneghinib, J.A.P. Aranhab, F. Saltarab
aDepartment of Mechanical Engineering, Mackenzie Presbyterian University, Rua da Consolacao, 930, Consolacao, São Paulo, 01302-907, Brazil bNDF, Department of Mechanical Engineering, University of São Paulo-USP, Butanta, 05508-900, Brazil
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ABSTRACT
The purpose of this study is to investigate the influence of the size of a discrete solenoidal subspace, generated by the kernel of the divergence operator, in the dynamic behavior of a stability problem. This problem is associated with the incompressible and viscous flow around a circular cylinder. The solenoidal subspaces were generated from the quadratic Taylor-Hood element for the velocity and the linear element for the pressure. These discrete subspaces were characterized according to their dimensions and their ability to catch the dynamics of the problem of linear stability.

Keywords:  Frechet operator; Hydrodynamic stability; Solenoidal subspace; Navier-Stokes; Finite element method; circular cylinder spectra
* Corresponding author. Tel.: + 55 (11) 3236 8756; E-mail: jihlopez@mackenzie.com.br