Hsu, M.-C.; Bazilevs, Y.; Calo, V. M.; Tezduyar, T. E.; Hughes, T. J. R. Improving stability of stabilized and multiscale formulations in flow simulations at small time steps. (English) Zbl 1406.76028 Comput. Methods Appl. Mech. Eng. 199, No. 13-16, 828-840 (2010). Summary: The objective of this paper is to show that use of the element-vector-based definition of stabilization parameters, introduced in [T. E. Tezduyar, Int. J. Numer. Methods Fluids 43, No. 5, 555–575 (2003; Zbl 1032.76605); T. E. Tezduyar and Y. Osawa, Comput. Methods Appl. Mech. Eng. 190, No. 3–4, 411–430 (2000; Zbl 0973.76057)], circumvents the well-known instability associated with conventional stabilized formulations at small time steps. We describe formulations for linear advection-diffusion and incompressible Navier-Stokes equations and test them on three benchmark problems: advection of an L-shaped discontinuity, laminar flow in a square domain at low Reynolds number, and turbulent channel flow at friction-velocity Reynolds number of 395. Cited in 142 Documents MSC: 76F65 Direct numerical and large eddy simulation of turbulence 76M30 Variational methods applied to problems in fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids Keywords:variational multiscale methods; stabilized methods; advection-diffusion equation; element-vector-based \(\tau \); incompressible Navier-Stokes equations; turbulence modeling; turbulent channel flow Citations:Zbl 1032.76605; Zbl 0973.76057 PDFBibTeX XMLCite \textit{M. C. Hsu} et al., Comput. Methods Appl. Mech. Eng. 199, No. 13--16, 828--840 (2010; Zbl 1406.76028) Full Text: DOI References: [1] Akkerman, I.; Bazilevs, Y.; Calo, V. M.; Hughes, T. 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