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A spectral collocation method for the Navier-Stokes equations. (English) Zbl 0573.76036

A Fourier-Chebyshev spectral method for the incompressible Navier-Stokes equations is described. It is applicable to a variety of problems including some with fluid properties which vary strongly both in the normal direction and in time. In this fully spectral algorithm, a preconditioned iterative technique is used for solving the implicit equations arising from semi-implicit treatment of pressure, mean advection, and vertical diffusion terms. The algorithm is tested by applying it to hydrodynamic stability problems in channel flow and in external boundary layers with both constant and variable viscosity.

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
76M99 Basic methods in fluid mechanics
76E99 Hydrodynamic stability
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