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Fourier/Chebyshev methods for the incompressible Navier-Stokes equations in infinite domains. (English) Zbl 0838.76058

A fully spectral method is presented for the unsteady Navier-Stokes equations which are infinite or semi-infinite in one dimension. The scheme assumes that the vorticity in the flow is essentially concentrated in a finite region, which is represented numerically by the standard spectral collocation methods. To accommodate the slow exponential decay of the velocity at infinity, extra expansion functions are introduced, which are handled analytically. A detailed error analysis is presented, and two applications to direct numerical simulation of turbulent flows are discussed. The numerical performance of the scheme is demonstrated for high Reynolds number incompressible flows.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76D05 Navier-Stokes equations for incompressible viscous fluids
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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[1] Rogallo, R. S.; Moin, P., Annu. Rev. Fluid Mech., 16, 99 (1984)
[2] Kim, J.; Moin, P.; Moser, R., J. Fluid. Mech., 177, 133 (1987)
[3] Laurien, E.; Kleiser, L., J. Fluid. Mech., 199, 403 (1989)
[4] Malik, M. R.; Zang, T. A.; Hussaini, M. Y., J. Comput. Phys., 61, 64 (1985)
[5] Spalart, P. R., NASA Technical Memorandum 88222 (1986), (unpublished)
[6] Spalart, P. R.; Moser, R. D.; Rogers, M. M., J. Comput. Phys., 96, 297 (1991)
[7] Agüí, J. C.; Jiménez, J., Technical Note ETSIA/ME-918, (Int. Symp. Parallel CFD. Int. Symp. Parallel CFD, Stuttgart (June 10-12, 1991)), School of Aeronautics, Madrid
[8] Corral, R.; Jiménez, J., (AGARD Symp. Transition and Turbulence. AGARD Symp. Transition and Turbulence, Chania, Crete (April 18-21, 1994)), 21.1
[9] Deville, M.; Kleiser, L.; Montigny-Rannou, F., Int. J. Numer. Methods Fluids, 4, 1149 (1984)
[10] Jiménez, J., J. Fluid Mech., 218, 265 (1990)
[11] Gottlieb, D.; Orszag, S. A., Numerical Analysis of Spectral Methods: Theory and Applications, (Regional Conference Series in Applied Mathematics, Vol. 26 (1977), SIAM: SIAM Philadelphia) · Zbl 0561.76076
[12] Couder, Y.; Basdevant, C., J. Fluid Mech., 173, 255 (1986)
[13] Jiménez, J.; Martel, C., Phys. Fluids A, 3, 1261 (1991)
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