variavel0=<b>Leandro Franco de Souza</b> - lefraso@zipmail.com.br ITA
<b>Marcio T. Mendonca</b> - marcio@iae.cta.be CTA
<b>Marcello A. Faraco de Medeiros</b> - marcello@sc.usp.br USP-SC
<b>Abstract.</b> This paper presents various finite differences schemes and compare their ability to simulate instability waves in a given flow fluid. The governing equations for two-dimensional, incompressible flows are derived in vorticity-velocity formulation. Four different space discretization schemes are tested, namely, a 2nd order central differences, a 4th order central differences, a 4th order compact scheme and a 6th order compact scheme. In time a classical 4th order Runge-Kutta scheme is used. The influence of a grid refinement in the streamwise and normal directions are evaluated. The results are compared against linear stability theory for the evolution of small ampitude Tollmien-Schlichting waves in a plane Poiseuille flow. Both the amplification rate and the wavenumber are considered as verification parameters, showing the degree of dissipation and dispersion introduced by the different numerical schemes. The results confirm that high order schemes are necessary for studying the hydrodynamic instabilities of this flow.
<b>Keywords.</b> high resolution finite differences, compact differences schemes, vorticity-velocity formulation, hydrodynamic instability, laminar flow transition to turbulence.