Improving stability of stabilized and multiscale formulations in flow simulations at small time steps

• Published in: Computer methods in applied mechanics and engineering 2010-02, Vol.199 (13), p.828-840
• Main Authors: Hsu, M.-C., Bazilevs, Y., Calo, V.M., Tezduyar, T.E., Hughes, T.J.R.
• Format: Article
• Language: English
• Subjects: Advection–diffusion equation; Computational techniques; Element-vector-based [formula omitted]; Exact sciences and technology; Flows in ducts, channels, nozzles, and conduits; Fluid dynamics; Fundamental areas of phenomenology (including applications); General theory; Incompressible Navier–Stokes equations; Mathematical methods in physics; Physics; Stabilized methods; Turbulence modeling; Turbulence simulation and modeling; Turbulent channel flow; Turbulent flows, convection, and heat transfer; Variational multiscale methods
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2009.06.019

The objective of this paper is to show that use of the element-vector-based definition of stabilization parameters, introduced in [T.E. Tezduyar, Computation of moving boundaries and interfaces and stabilization parameters, Int. J. Numer. Methods Fluids 43 (2003) 555–575; T.E. Tezduyar, Y. Osawa, Finite element stabilization parameters computed from element matrices and vectors, Comput. Methods Appl. Mech. Engrg. 190 (2000) 411–430], 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.