Prediction of flow instabilities and transition using high-resolution methods

S. Patel, D. Drikakis

Research output: Contribution to conferencePaper

1 Citation (Scopus)

Abstract

We have considered the problem of flow through a rectangular channel with a suddenly-expanded and suddenly-contracted part and have conducted a computational investigation to examine numerical effects on the prediction of flow instabilities and bifurcation phenomena for both fine-resolved and under-resolved grid computations. The results revealed that the solution of the flow depends on the numerical method employed especially in the case for under-resolved grid computations. We have employed high-resolution (Godunov-type) methods in conjunction with first-, second- and third-order accurate interpolation schemes. It is shown that the order of accuracy of the interpolation used in the discretisation of the wave-speed dependent term (non-linear dissipation term) and averaged part of the intercell flux affects the prediction of the instability. Computations using first-order discretisation for the calculation of the flux components results in symmetric stable flow for all schemes except one (the characteristics-based scheme), whereas second- and third-order discretisations lead to a symmetry breaking bifurcation for all schemes within a critical range of Reynolds numbers. The results obtained for all numerical schemes confirm that the flow is steady and symmetric at low Reynolds numbers, becomes asymmetric at a critical Reynolds number then regains symmetry at another critical Reynolds number. In under-resolved grid computations the onset of symmetry breaking bifurcation is different for each numerical scheme and the degree of asymmetry is strongly dependent on the non-linear dissipation of the numerical scheme employed. Fine-resolved simulations showed little difference in the degree of asymmetry predicted by the three numerical schemes employed.
LanguageEnglish
Number of pages12
Publication statusPublished - 28 Jul 2004
EventECCOMAS 2004 - Jyväskylä, Finland
Duration: 24 Jul 200428 Jul 2004

Conference

ConferenceECCOMAS 2004
CityJyväskylä, Finland
Period24/07/0428/07/04

Fingerprint

Flow Instability
Numerical Scheme
High Resolution
Nonlinear Dissipation
Reynolds number
Bifurcation
Prediction
Discretization
Grid
Symmetry Breaking
Asymmetry
Interpolate
Dependent
Wave Speed
Low Reynolds number
Term
Numerical Methods
First-order
Symmetry
Range of data

Keywords

  • asymmetries
  • high-resolution methods
  • incompressible flow
  • instabilities
  • bifurcation phenomena
  • computational investigation
  • critical Reynolds number

Cite this

Patel, S., & Drikakis, D. (2004). Prediction of flow instabilities and transition using high-resolution methods. Paper presented at ECCOMAS 2004, Jyväskylä, Finland, .
Patel, S. ; Drikakis, D. / Prediction of flow instabilities and transition using high-resolution methods. Paper presented at ECCOMAS 2004, Jyväskylä, Finland, .12 p.
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Patel, S & Drikakis, D 2004, 'Prediction of flow instabilities and transition using high-resolution methods' Paper presented at ECCOMAS 2004, Jyväskylä, Finland, 24/07/04 - 28/07/04, .

Prediction of flow instabilities and transition using high-resolution methods. / Patel, S.; Drikakis, D.

2004. Paper presented at ECCOMAS 2004, Jyväskylä, Finland, .

Research output: Contribution to conferencePaper

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T1 - Prediction of flow instabilities and transition using high-resolution methods

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AU - Drikakis, D.

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N2 - We have considered the problem of flow through a rectangular channel with a suddenly-expanded and suddenly-contracted part and have conducted a computational investigation to examine numerical effects on the prediction of flow instabilities and bifurcation phenomena for both fine-resolved and under-resolved grid computations. The results revealed that the solution of the flow depends on the numerical method employed especially in the case for under-resolved grid computations. We have employed high-resolution (Godunov-type) methods in conjunction with first-, second- and third-order accurate interpolation schemes. It is shown that the order of accuracy of the interpolation used in the discretisation of the wave-speed dependent term (non-linear dissipation term) and averaged part of the intercell flux affects the prediction of the instability. Computations using first-order discretisation for the calculation of the flux components results in symmetric stable flow for all schemes except one (the characteristics-based scheme), whereas second- and third-order discretisations lead to a symmetry breaking bifurcation for all schemes within a critical range of Reynolds numbers. The results obtained for all numerical schemes confirm that the flow is steady and symmetric at low Reynolds numbers, becomes asymmetric at a critical Reynolds number then regains symmetry at another critical Reynolds number. In under-resolved grid computations the onset of symmetry breaking bifurcation is different for each numerical scheme and the degree of asymmetry is strongly dependent on the non-linear dissipation of the numerical scheme employed. Fine-resolved simulations showed little difference in the degree of asymmetry predicted by the three numerical schemes employed.

AB - We have considered the problem of flow through a rectangular channel with a suddenly-expanded and suddenly-contracted part and have conducted a computational investigation to examine numerical effects on the prediction of flow instabilities and bifurcation phenomena for both fine-resolved and under-resolved grid computations. The results revealed that the solution of the flow depends on the numerical method employed especially in the case for under-resolved grid computations. We have employed high-resolution (Godunov-type) methods in conjunction with first-, second- and third-order accurate interpolation schemes. It is shown that the order of accuracy of the interpolation used in the discretisation of the wave-speed dependent term (non-linear dissipation term) and averaged part of the intercell flux affects the prediction of the instability. Computations using first-order discretisation for the calculation of the flux components results in symmetric stable flow for all schemes except one (the characteristics-based scheme), whereas second- and third-order discretisations lead to a symmetry breaking bifurcation for all schemes within a critical range of Reynolds numbers. The results obtained for all numerical schemes confirm that the flow is steady and symmetric at low Reynolds numbers, becomes asymmetric at a critical Reynolds number then regains symmetry at another critical Reynolds number. In under-resolved grid computations the onset of symmetry breaking bifurcation is different for each numerical scheme and the degree of asymmetry is strongly dependent on the non-linear dissipation of the numerical scheme employed. Fine-resolved simulations showed little difference in the degree of asymmetry predicted by the three numerical schemes employed.

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KW - high-resolution methods

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KW - critical Reynolds number

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Patel S, Drikakis D. Prediction of flow instabilities and transition using high-resolution methods. 2004. Paper presented at ECCOMAS 2004, Jyväskylä, Finland, .