Analysis of Hybrid Algorithms for the Navier-Stokes Equations with respect to Hydrodynamic Stability Theory

Hybrid three-dimensional algorithms for the numerical integration of the incompressible Navier–Stokes equations are analyzed with respect to hydrodynamic stability in both linear and nonlinear fields. The computational schemes are mixed—spectral and finite differences—and are applied to the case of the channel flow driven by constant pressure gradient; time marching is handled with the fractional step method. Different formulations—fully explicit convective term, partially and fully implicit viscous term combined with uniform, stretched, staggered and non-staggered meshes, x-velocity splitted and non-splitted in average and perturbation component – are analyzed by monitoring the evolution in time of both small and finite amplitude perturbations of the mean flow. The results in the linear feld are compared with correspondent solutions of the Orr–Sommerfeld equation; in the nonlinear feld, the comparison is made with results obtained by other authors.