variavel0=<b>Leandro F. Souza</b> - lefraso@zipmail.com.br ITA
<b>Marcio T. Mendonca</b> - marcio@iae.cta.br CTA
<b>Marcello A. Faraco Medeiros</b> - marcello@sc.usp.br USP-SC
<b>Markus Kloker</b> - mkloker@iag.uni-stuttgart.de University of Stuttgart
<b>Abstract.</b> A numerical method for accurately solving the incompressible Navier-Stokes equation in vorticity-velocity formulation is presented. The governing equations are discretized using a sixth order compact finite differences scheme for the spatial derivatives. The Poisson equation for the normal velocity component is solved by an iterative Line Successive Over Relaxation Method using a multigrid Full Approximation Scheme to accelerate the convergence. Results are presented for the spatial evolution of two-dimensional Tollmien-Schlichting waves on a flat plate boundary layer with a very small disturbance amplitude. Growth rates, phase and eigen functions are compared with results from Linear Stability Theory, providing a through check of the numerical method. Finite amplitude disturbances are also considered. The main interest in a two-dimensional nonlinear instability analysis is to use it as a step toward a three dimensional code. Nonlinear results are compared against results obtained from a code based on the Parabolized Stability Equations.
<b>Keywords.</b> boundary layer stability, compact differences schemes, vorticity velocity formulation, hydrodynamic instability, laminar flow transition.