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 - <p style="text-align: justify;">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.</p>