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

Abstract
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. © 2009 Elsevier B.V. All rights reserved.

Citation
Hsu, M.-C., Bazilevs, Y., Calo, V. M., Tezduyar, T. E., & Hughes, T. J. R. (2010). Improving stability of stabilized and multiscale formulations in flow simulations at small time steps. Computer Methods in Applied Mechanics and Engineering, 199(13-16), 828–840. doi:10.1016/j.cma.2009.06.019

Acknowledgements
We wish to thank the Texas Advanced Computing Center (TACC) at the University of Texas at Austin for providing HPC resources that have contributed to the research results reported within this paper. Support of Teragrid Grant No. MCAD7S032 is also gratefully acknowledged.

Publisher
Elsevier BV

Journal
Computer Methods in Applied Mechanics and Engineering

DOI
10.1016/j.cma.2009.06.019

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