Improved discontinuity-capturing finite element techniques for reaction effects in turbulence computation

A. Corsini, F. Rispoli, A. Santoriello, Tayfun E. Tezduyar

Research output: Contribution to journalArticle

70 Citations (Scopus)

Abstract

Recent advances in turbulence modeling brought more and more sophisticated turbulence closures (e.g. k-ε, k-ε -v 2-f, Second Moment Closures), where the governing equations for the model parameters involve advection, diffusion and reaction terms. Numerical instabilities can be generated by the dominant advection or reaction terms. Classical stabilized formulations such as the Streamline-Upwind/Petrov-Galerkin (SUPG) formulation (Brook and Hughes, comput methods Appl Mech Eng 32:199-255, 1982; Hughes and Tezduyar, comput methods Appl Mech Eng 45: 217-284, 1984) are very well suited for preventing the numerical instabilities generated by the dominant advection terms. A different stabilization however is needed for instabilities due to the dominant reaction terms. An additional stabilization term, called the diffusion for reaction-dominated (DRD) term, was introduced by Tezduyar and Park (comput methods Appl Mech Eng 59:307-325, 1986) for that purpose and improves the SUPG performance. In recent years a new class of variational multi-scale (VMS) stabilization (Hughes, comput methods Appl Mech Eng 127:387-401, 1995) has been introduced, and this approach, in principle, can deal with advection-diffusion- reaction equations. However, it was pointed out in Hanke (comput methods Appl Mech Eng 191:2925-2947) that this class of methods also need some improvement in the presence of high reaction rates. In this work we show the benefits of using the DRD operator to enhance the core stabilization techniques such as the SUPG and VMS formulations. We also propose a new operator called the DRDJ (DRD with the local variation jump) term, targeting the reduction of numerical oscillations in the presence of both high reaction rates and sharp solution gradients. The methods are evaluated in the context of two stabilized methods: the classical SUPG formulation and a recently-developed VMS formulation called the V-SGS (Corsini et al. comput methods Appl Mech Eng 194:4797-4823, 2005). Model problems and industrial test cases are computed to show the potential of the proposed methods in simulation of turbulent flows.

Original languageEnglish
Pages (from-to)356-364
Number of pages9
JournalComputational Mechanics
Volume38
Issue number4-5
DOIs
Publication statusPublished - 2006 Sep
Externally publishedYes

Fingerprint

Advection
Turbulence
Discontinuity
Finite Element
Stabilization
Petrov-Galerkin
Streamlines
Term
Reaction rates
Formulation
Numerical Instability
Reaction Rate
Turbulent flow
Moment Closure
Advection-diffusion-reaction Equation
Stabilized Methods
Turbulence Modeling
Advection-diffusion
Operator
Turbulent Flow

Keywords

  • Discontinuities
  • Finite element
  • Variational method

ASJC Scopus subject areas

  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

Cite this

Improved discontinuity-capturing finite element techniques for reaction effects in turbulence computation. / Corsini, A.; Rispoli, F.; Santoriello, A.; Tezduyar, Tayfun E.

In: Computational Mechanics, Vol. 38, No. 4-5, 09.2006, p. 356-364.

Research output: Contribution to journalArticle

@article{73b4715053074286ab54a90b1c10e16a,
title = "Improved discontinuity-capturing finite element techniques for reaction effects in turbulence computation",
abstract = "Recent advances in turbulence modeling brought more and more sophisticated turbulence closures (e.g. k-ε, k-ε -v 2-f, Second Moment Closures), where the governing equations for the model parameters involve advection, diffusion and reaction terms. Numerical instabilities can be generated by the dominant advection or reaction terms. Classical stabilized formulations such as the Streamline-Upwind/Petrov-Galerkin (SUPG) formulation (Brook and Hughes, comput methods Appl Mech Eng 32:199-255, 1982; Hughes and Tezduyar, comput methods Appl Mech Eng 45: 217-284, 1984) are very well suited for preventing the numerical instabilities generated by the dominant advection terms. A different stabilization however is needed for instabilities due to the dominant reaction terms. An additional stabilization term, called the diffusion for reaction-dominated (DRD) term, was introduced by Tezduyar and Park (comput methods Appl Mech Eng 59:307-325, 1986) for that purpose and improves the SUPG performance. In recent years a new class of variational multi-scale (VMS) stabilization (Hughes, comput methods Appl Mech Eng 127:387-401, 1995) has been introduced, and this approach, in principle, can deal with advection-diffusion- reaction equations. However, it was pointed out in Hanke (comput methods Appl Mech Eng 191:2925-2947) that this class of methods also need some improvement in the presence of high reaction rates. In this work we show the benefits of using the DRD operator to enhance the core stabilization techniques such as the SUPG and VMS formulations. We also propose a new operator called the DRDJ (DRD with the local variation jump) term, targeting the reduction of numerical oscillations in the presence of both high reaction rates and sharp solution gradients. The methods are evaluated in the context of two stabilized methods: the classical SUPG formulation and a recently-developed VMS formulation called the V-SGS (Corsini et al. comput methods Appl Mech Eng 194:4797-4823, 2005). Model problems and industrial test cases are computed to show the potential of the proposed methods in simulation of turbulent flows.",
keywords = "Discontinuities, Finite element, Variational method",
author = "A. Corsini and F. Rispoli and A. Santoriello and Tezduyar, {Tayfun E.}",
year = "2006",
month = "9",
doi = "10.1007/s00466-006-0045-x",
language = "English",
volume = "38",
pages = "356--364",
journal = "Computational Mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
number = "4-5",

}

TY - JOUR

T1 - Improved discontinuity-capturing finite element techniques for reaction effects in turbulence computation

AU - Corsini, A.

AU - Rispoli, F.

AU - Santoriello, A.

AU - Tezduyar, Tayfun E.

PY - 2006/9

Y1 - 2006/9

N2 - Recent advances in turbulence modeling brought more and more sophisticated turbulence closures (e.g. k-ε, k-ε -v 2-f, Second Moment Closures), where the governing equations for the model parameters involve advection, diffusion and reaction terms. Numerical instabilities can be generated by the dominant advection or reaction terms. Classical stabilized formulations such as the Streamline-Upwind/Petrov-Galerkin (SUPG) formulation (Brook and Hughes, comput methods Appl Mech Eng 32:199-255, 1982; Hughes and Tezduyar, comput methods Appl Mech Eng 45: 217-284, 1984) are very well suited for preventing the numerical instabilities generated by the dominant advection terms. A different stabilization however is needed for instabilities due to the dominant reaction terms. An additional stabilization term, called the diffusion for reaction-dominated (DRD) term, was introduced by Tezduyar and Park (comput methods Appl Mech Eng 59:307-325, 1986) for that purpose and improves the SUPG performance. In recent years a new class of variational multi-scale (VMS) stabilization (Hughes, comput methods Appl Mech Eng 127:387-401, 1995) has been introduced, and this approach, in principle, can deal with advection-diffusion- reaction equations. However, it was pointed out in Hanke (comput methods Appl Mech Eng 191:2925-2947) that this class of methods also need some improvement in the presence of high reaction rates. In this work we show the benefits of using the DRD operator to enhance the core stabilization techniques such as the SUPG and VMS formulations. We also propose a new operator called the DRDJ (DRD with the local variation jump) term, targeting the reduction of numerical oscillations in the presence of both high reaction rates and sharp solution gradients. The methods are evaluated in the context of two stabilized methods: the classical SUPG formulation and a recently-developed VMS formulation called the V-SGS (Corsini et al. comput methods Appl Mech Eng 194:4797-4823, 2005). Model problems and industrial test cases are computed to show the potential of the proposed methods in simulation of turbulent flows.

AB - Recent advances in turbulence modeling brought more and more sophisticated turbulence closures (e.g. k-ε, k-ε -v 2-f, Second Moment Closures), where the governing equations for the model parameters involve advection, diffusion and reaction terms. Numerical instabilities can be generated by the dominant advection or reaction terms. Classical stabilized formulations such as the Streamline-Upwind/Petrov-Galerkin (SUPG) formulation (Brook and Hughes, comput methods Appl Mech Eng 32:199-255, 1982; Hughes and Tezduyar, comput methods Appl Mech Eng 45: 217-284, 1984) are very well suited for preventing the numerical instabilities generated by the dominant advection terms. A different stabilization however is needed for instabilities due to the dominant reaction terms. An additional stabilization term, called the diffusion for reaction-dominated (DRD) term, was introduced by Tezduyar and Park (comput methods Appl Mech Eng 59:307-325, 1986) for that purpose and improves the SUPG performance. In recent years a new class of variational multi-scale (VMS) stabilization (Hughes, comput methods Appl Mech Eng 127:387-401, 1995) has been introduced, and this approach, in principle, can deal with advection-diffusion- reaction equations. However, it was pointed out in Hanke (comput methods Appl Mech Eng 191:2925-2947) that this class of methods also need some improvement in the presence of high reaction rates. In this work we show the benefits of using the DRD operator to enhance the core stabilization techniques such as the SUPG and VMS formulations. We also propose a new operator called the DRDJ (DRD with the local variation jump) term, targeting the reduction of numerical oscillations in the presence of both high reaction rates and sharp solution gradients. The methods are evaluated in the context of two stabilized methods: the classical SUPG formulation and a recently-developed VMS formulation called the V-SGS (Corsini et al. comput methods Appl Mech Eng 194:4797-4823, 2005). Model problems and industrial test cases are computed to show the potential of the proposed methods in simulation of turbulent flows.

KW - Discontinuities

KW - Finite element

KW - Variational method

UR - http://www.scopus.com/inward/record.url?scp=33745651828&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33745651828&partnerID=8YFLogxK

U2 - 10.1007/s00466-006-0045-x

DO - 10.1007/s00466-006-0045-x

M3 - Article

AN - SCOPUS:33745651828

VL - 38

SP - 356

EP - 364

JO - Computational Mechanics

JF - Computational Mechanics

SN - 0178-7675

IS - 4-5

ER -