Loading [MathJax]/jax/output/HTML-CSS/config.js
full
search.png

Search

close.png

Cancel

arrow
Volume 22, Issue 2
On a 1/2-Equation Model of Turbulence

Rui Fang, Wei-Wei Han & William J Layton

DOI: 10.4208/ijnam2025-1007

Int. J. Numer. Anal. Mod., 22 (2025), pp. 139-156.

Published online: 2025-02

Preview Purchase PDF 191 2606

Cited by

google scholar semantic scholar
Export citation
  • Abstract

In 1-equation URANS models of turbulence, the eddy viscosity is given by $\nu_T = 0.55l(x, t)\sqrt{k(x, t)}.$ The length scale $l$ must be pre-specified and $k(x, t)$ is determined by solving a nonlinear partial differential equation. We show that in interesting cases the spacial mean of $k(x, t)$ satisfies a simple ordinary differential equation. Using its solution in $\nu_T$ results in a 1/2-equation model. This model has attractive analytic properties. Further, in comparative tests in 2d and 3d the velocity statistics produced by the 1/2-equation model are comparable to those of the full 1-equation model.

  • Keywords

Turbulence, eddy viscosity model, and 1-equation model.

  • AMS Subject Headings

35R35, 49J40, 60G40

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{IJNAM-22-139, author = {Fang , RuiHan , Wei-Wei and Layton , William J}, title = {On a 1/2-Equation Model of Turbulence}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2025}, volume = {22}, number = {2}, pages = {139--156}, abstract = {

In 1-equation URANS models of turbulence, the eddy viscosity is given by $\nu_T = 0.55l(x, t)\sqrt{k(x, t)}.$ The length scale $l$ must be pre-specified and $k(x, t)$ is determined by solving a nonlinear partial differential equation. We show that in interesting cases the spacial mean of $k(x, t)$ satisfies a simple ordinary differential equation. Using its solution in $\nu_T$ results in a 1/2-equation model. This model has attractive analytic properties. Further, in comparative tests in 2d and 3d the velocity statistics produced by the 1/2-equation model are comparable to those of the full 1-equation model.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2025-1007}, url = {http://global-sci.org/intro/article_detail/ijnam/23818.html} }
TY - JOUR T1 - On a 1/2-Equation Model of Turbulence AU - Fang , Rui AU - Han , Wei-Wei AU - Layton , William J JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 139 EP - 156 PY - 2025 DA - 2025/02 SN - 22 DO - http://doi.org/10.4208/ijnam2025-1007 UR - https://global-sci.org/intro/article_detail/ijnam/23818.html KW - Turbulence, eddy viscosity model, and 1-equation model. AB -

In 1-equation URANS models of turbulence, the eddy viscosity is given by $\nu_T = 0.55l(x, t)\sqrt{k(x, t)}.$ The length scale $l$ must be pre-specified and $k(x, t)$ is determined by solving a nonlinear partial differential equation. We show that in interesting cases the spacial mean of $k(x, t)$ satisfies a simple ordinary differential equation. Using its solution in $\nu_T$ results in a 1/2-equation model. This model has attractive analytic properties. Further, in comparative tests in 2d and 3d the velocity statistics produced by the 1/2-equation model are comparable to those of the full 1-equation model.

Fang , RuiHan , Wei-Wei and Layton , William J. (2025). On a 1/2-Equation Model of Turbulence. International Journal of Numerical Analysis and Modeling. 22 (2). 139-156. doi:10.4208/ijnam2025-1007
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard