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

Ming-Chen Hsu; Yuri Bazilevs; Victor M. Calo; Tayfun E. Tezduyar; Thomas Jr R Hughes

doi:10.1016/j.cma.2009.06.019

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

Ming-Chen Hsu, Yuri Bazilevs, Victor M. Calo, Tayfun E. Tezduyar, Thomas Jr R Hughes

Research output: Contribution to journal › Article › peer-review

207 Scopus citations

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.

Original language	English (US)
Pages (from-to)	828-840
Number of pages	13
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	199
Issue number	13-16
DOIs	https://doi.org/10.1016/j.cma.2009.06.019
State	Published - Feb 2010

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
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.

ASJC Scopus subject areas

General Physics and Astronomy
Mechanics of Materials
Mechanical Engineering
Computational Mechanics
Computer Science Applications

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10.1016/j.cma.2009.06.019

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title = "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. {\textcopyright} 2009 Elsevier B.V. All rights reserved.",

author = "Ming-Chen Hsu and Yuri Bazilevs and Calo, {Victor M.} and Tezduyar, {Tayfun E.} and Hughes, {Thomas Jr R}",

note = "KAUST Repository Item: Exported on 2020-10-01 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.",

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AU - Hughes, Thomas Jr R

N1 - KAUST Repository Item: Exported on 2020-10-01 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.

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N2 - 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.

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

Abstract

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