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Improving stability of stabilized and multiscale formulations in flow simulations at small time steps. (English) Zbl 1406.76028
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.

##### 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
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