**Author details**

*u* ′ *ij* ¯

pressible flow are as follows:

334 Numerical Simulation - From Brain Imaging to Turbulent Flows

In the Eqs. (1.27) and (1.28), *u*¯*<sup>i</sup>*

positions *xi*

follows:

*vt*

≠0. In general, the use or the LES technique has produced better results in flow simula‐ tions when RANS models usually fail, like turbulent boundary layers subjected to adverse pressure gradients, the prediction of drag coefficients for immerse bodies in periodic re‐ gimes [21] and other unsteady flows. Governing equations for the LES model in an incom‐

*x* (1.27)

(1.28)

<sup>0</sup> ¶ <sup>=</sup> ¶ *i i u*

¶ ¶ ¶¶ ¶ ¶ 1 é ù + =- - + ê ú ¶ ¶ ¶¶ ¶ ¶ ê ú ë û *i j ij i i j ijj j*

t

( 1,2,3) *i* =

kinematic viscosity and density, respectively. Regarding the local influence of the Reynolds stresses, one of the most used models is the classic Smagorinsky model, which is expressed as

the subgrid scale turbulent viscosity, "*Δ*¯"the filter characteristic length. Generally, the size

Originally, RANS models were conceived to include the turbulence average effect in the Navier–Stokes equations solution. Therefore, they are widely recommended to simulate steady-state fully developed turbulent flows, being especially good reproducing off-wall phenomena. When the problem needed to solve is highly depended on the adequate prediction of pressures and forces on the wall, it is recommended to apply functions for

, where *P*¯ represents the filtered pressure component, "*<sup>v</sup>*" and "*ρ*" represent the

n

represents the filtered velocity components at different Cartesian

*ij i j i j* = - *uu uu* (1.29)

*S C SS* (1.30)

*ij* the filtered strain tensor,

1/3, and the Smagorinsky

*ij*, being *S*¯

*ijS*¯

*uP u u u t x xx x x*

r

t

t

constant *Cs* can be varied from 0.05 to 0.1 [22].

 td

of the filter is proportional to the volume "Ω" of the cell Δ¯ =2(*Ω*)

**6. RANS and LES capacities for turbulent flows analysis**

where the strain tensor of the fluid in each cell is ‖S‖<sup>=</sup> <sup>2</sup>*S*¯

( ) <sup>1</sup> <sup>2</sup> 2 2 || <sup>3</sup> - = - <sup>=</sup> D- || *ij kk ij t ij <sup>s</sup> ij*

 n

> Alejandro Alonzo-García1,2, Claudia del Carmen Gutiérrez-Torres3\* and José Alfredo Jiménez-Bernal3

\*Address all correspondence to: claudia2174@yahoo.com

1 Centro de Investigación Científica de Yucatán, A.C, Mexico

2 Tecnológico Nacional de México, Instituto Tecnológico de Mérida, Mexico

3 Instituto Politecnico Nacional, SEPI-ESIME Zacatenco, Mexico City, Mexico
