×

zbMATH — the first resource for mathematics

Spectral element-Fourier methods for incompressible turbulent flows. (English) Zbl 0722.76053
Summary: A mixed spectral element-(Fourier) spectral method is proposed for solution of the incompressible Navier-Stokes equations in general, curvilinear domains. The formulation is appropriate for simulations of turbulent flows in complex geometries with only one homogeneous flow direction. The governing equations are written in a form suitable for both direct (DNS) and large-eddy (LES) simulations allowing a unified implementation. The method is based on skew-symmetric convective operators that induce minimal aliasing errors and fast Helmholtz solvers that employ efficient iterative algorithms (e.g. multigrid). Direct numerical simulations of channel flow verified that the proposed method can sustain turbulent fluctuations even at ‘marginal’ Reynolds numbers. The flexibility of the method to efficiently simulate complex-geometry flows is demonstrated through an example of transitional flow in a grooved channel and an example of transitional-turbulent flow over rough wall surfaces.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76F99 Turbulence
76D05 Navier-Stokes equations for incompressible viscous fluids
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Hussaini, M.Y.; Zang, T.A., Spectral methods in fluid dynamics, Ann. rev. fluid mech., 19, 339-367, (1987) · Zbl 0636.76009
[2] Kim, J.; Moin, P.; Moser, R., Turbulence statistics in fully developed channel flow at low Reynolds number, J. fluid mech., 177, 133-166, (1987) · Zbl 0616.76071
[3] Patera, A.T., A spectral element method for fluid dynamics: laminar flow in a channel expansion, J. comput. phys., 54, 468-488, (1984) · Zbl 0535.76035
[4] Karniadakis, G.E.; Mikic, B.B.; Patera, A.T., Minimum-dissipation transport enhancement by flow destabilization: Reynolds’ analogy revisited, J. fluid mech., 192, 365-391, (1988)
[5] Karniadakis, G.E., Spectral element simulations of laminar and turbulent flows in complex geometries, Appl. numer. math., 6, 85-105, (1989) · Zbl 0678.76050
[6] Fischer, P.; Ho, L.W.; Karniadakis, G.E.; Ronquist, E.; Patera, A.T., Recent advances in parallel spectral element simulation of unsteady incompressible flows, Comput. & structures, 30, 217-231, (1988) · Zbl 0668.76039
[7] Ronquist, E.M., Optimal spectral element methods for the unsteady three-dimensional incompressible Navier-Stokes equations, (1988), Massachusetts Institute of Technology
[8] Yakhot, V.; Orszag, S.A., Renormalization group formulation of large eddy simulation, (), 155-174 · Zbl 0647.76041
[9] Orszag, S.A.; Israeli, M.; Deville, M.O., Boundary condition for incompressible flows, J. sci. comp., 1, 1, 75-111, (1985)
[10] Karniadakis, G.E.; Israeli, M.; Orszag, S.A., High-order splitting methods for the incompressible Navier-Stokes equations, J. comput. phys., (1990), to appear
[11] Ghaddar, N.K.; Korczak, K.Z.; Mikic, B.B.; Patera, A.T., Numerical investigation of incompressible flow in grooved channels: part 1. stability and self-sustained oscillation, J. fluid mech., 163, 99-127, (1986)
[12] Karniadakis, G.E.; Amon, C., Stability calculations of wall-bounded flows in complex geometry, (), 525-532
[13] Amon, C.; Patera, A.T., Numerical calculation of stable three-dimensional tertiary states in grooved-channel flow, Phys. fluids A, 1, 12, (2005-2009)
[14] Walsh, M.J., Turbulent boundary layer drag reduction using riblets, ()
[15] Wallace, J.M.; Balint, J.L., Viscous drag reduction using streamwise aligned riblets: survey and new results, (), 133-147
[16] Rai, M.M.; Moin, P., Direct simulations of turbulent flow using finite-difference schemes, () · Zbl 0726.76072
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.