Author(s): Giuseppe Passoni; Giancarlo Alfonsi; Massimo Galbiati
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Keywords: Navier-Stokes equations; Hydrodynamic stability theory
Abstract: The accuracy properties of two different discrete formulations for the time integration of the three-dimensional incompressible Navier-Stokes equations, are considered. The computational schemes are mixed, spectral and finite differences in space and semi-implicit in time; for time marching the fractional step method is used. The system of nonlinear partial differential equations of viscous fluid flow is integrated in time in the case of the plane channel and the properties of the numerical algorithms are studied by mainly monitoring their behavior with respect to the hydrodynamic stability theory. Two different formulations are considered. In the first scheme the convective terms and the viscous terms in and are incorporated in a fourth-order Runge-Kutta algorithm, while second-order centered finite difference implicit schemes are used to handle the viscous term in the direction orthogonal to the solid walls. In the second scheme the convective terms are handled by means of a thirdorder Runge-Kutta and the whole diffusive term with a Crank-Nicolson algorithm. The evolution in time of small amplitude perturbations of the mean flow is reported with different numbers of grid points along the direction.
Year: 1999