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Volume 19, Issue 2-3
Clipping over Dissipation in Turbulence Models

Kiera Kean, William Layton & Michael Schneier

Int. J. Numer. Anal. Mod., 19 (2022), pp. 424-438.

Published online: 2022-04

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  • Abstract

Clipping refers to adding 1 line of code $A ⇐ {\rm min}\{A, B\}$ to force the variable $A$ to stay below a present bound $B.$ Phenomenological clipping also occurs in turbulence models to correct for over dissipation caused by the action of eddy viscosity terms in regions of small scales. Herein we analyze eddy viscosity model energy dissipation rates with 2 phenomenological clipping strategies. Since the true Reynolds stresses are $O(d^2)$ ($d$ = wall normal distance) in the near wall region, the first is to force this near wall behavior in the eddy viscosity by $ν_{turb}⇐ {\rm min}\{ν_{turb}, \frac{\kappa}{T_{ref}}d^2\}$ for some preset $\kappa$ and time scale $T_{ref}.$ The second is Escudier’s early proposal to clip the turbulence length scale in a common specification of $ν_{turb},$ reducing too large values in the interior of the flow. Analyzing respectively shear flow turbulence and turbulence in a box (i.e., periodic boundary conditions), we show that both clipping strategies do prevent aggregate over dissipation of model solutions.

  • AMS Subject Headings

76F02, 76F10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-19-424, author = {Kean , KieraLayton , William and Schneier , Michael}, title = {Clipping over Dissipation in Turbulence Models}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2022}, volume = {19}, number = {2-3}, pages = {424--438}, abstract = {

Clipping refers to adding 1 line of code $A ⇐ {\rm min}\{A, B\}$ to force the variable $A$ to stay below a present bound $B.$ Phenomenological clipping also occurs in turbulence models to correct for over dissipation caused by the action of eddy viscosity terms in regions of small scales. Herein we analyze eddy viscosity model energy dissipation rates with 2 phenomenological clipping strategies. Since the true Reynolds stresses are $O(d^2)$ ($d$ = wall normal distance) in the near wall region, the first is to force this near wall behavior in the eddy viscosity by $ν_{turb}⇐ {\rm min}\{ν_{turb}, \frac{\kappa}{T_{ref}}d^2\}$ for some preset $\kappa$ and time scale $T_{ref}.$ The second is Escudier’s early proposal to clip the turbulence length scale in a common specification of $ν_{turb},$ reducing too large values in the interior of the flow. Analyzing respectively shear flow turbulence and turbulence in a box (i.e., periodic boundary conditions), we show that both clipping strategies do prevent aggregate over dissipation of model solutions.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/20489.html} }
TY - JOUR T1 - Clipping over Dissipation in Turbulence Models AU - Kean , Kiera AU - Layton , William AU - Schneier , Michael JO - International Journal of Numerical Analysis and Modeling VL - 2-3 SP - 424 EP - 438 PY - 2022 DA - 2022/04 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/20489.html KW - Energy dissipation rate, turbulence. AB -

Clipping refers to adding 1 line of code $A ⇐ {\rm min}\{A, B\}$ to force the variable $A$ to stay below a present bound $B.$ Phenomenological clipping also occurs in turbulence models to correct for over dissipation caused by the action of eddy viscosity terms in regions of small scales. Herein we analyze eddy viscosity model energy dissipation rates with 2 phenomenological clipping strategies. Since the true Reynolds stresses are $O(d^2)$ ($d$ = wall normal distance) in the near wall region, the first is to force this near wall behavior in the eddy viscosity by $ν_{turb}⇐ {\rm min}\{ν_{turb}, \frac{\kappa}{T_{ref}}d^2\}$ for some preset $\kappa$ and time scale $T_{ref}.$ The second is Escudier’s early proposal to clip the turbulence length scale in a common specification of $ν_{turb},$ reducing too large values in the interior of the flow. Analyzing respectively shear flow turbulence and turbulence in a box (i.e., periodic boundary conditions), we show that both clipping strategies do prevent aggregate over dissipation of model solutions.

Kiera Kean, William Layton & Michael Schneier. (2022). Clipping over Dissipation in Turbulence Models. International Journal of Numerical Analysis and Modeling. 19 (2-3). 424-438. doi:
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