View source for Analysis of Step 3

The main difference between this step and the previous one, is that now '''species and heat diffusion are additionally
taken into account in an inhomogeneous environment'''. Neither analytical nor reference solution are available for this
configuration, so that only comparisons between the three codes involved in the benchmark are possible.
Compared to '''Step 2''', the presence of '''high-temperature regions''' additionally modifies the '''evolution''' of the '''TGV'''
with time, '''turbulence''' being locally damped due to '''dilatation''' and '''higher viscosities'''. As a consequence, the needed
resolution for this case is less than in '''Step 2''': '''YALES2''' and '''DINO''' used only 256 grid points in each direction while
'''Nek5000''' used 36 elements (again with 7 Gauss-Lobatto-Legendre points in each element), i.e. 252 points in each
direction.

The results that will be compared involve:

1. '''Velocity profiles''' at <math>t = 2 \tau_{ref} = 0.5 ms</math> along the centerlines of the domain, as shown in Fig. 7;

2. '''Profiles''' of <math>H_2</math> and <math>O_2</math> '''mass fractions''' and '''profile of temperature''' at <math>t = 2 \tau_{ref} = 0.5 ms</math> along the y-centerline of
the domain, as illustrated in Figs. 8 and 9;

3. '''Evolution of maximal temperature''' in the domain vs. '''time''', as depicted in Fig. 10.

Looking at the results of '''velocity''' (Fig. 7) at time <math>t = 2 \tau_{ref} = 0.5 ms</math> along the centerlines of the computational domain,
it is observed that the three codes deliver the same '''velocity profiles'''; the agreement is visually perfect.
The results for the two main species '''mass fractions''' (<math>Y_{H2}</math>
and <math>Y_{O2}</math>) are also in excellent agreement among the
three participating codes, as it can be observed from Fig. 8.

[[File:vx_x_3d_nonreacting.png|250px]]
[[File:vy_y_3d_nonreacting.png|250px]]
[[File:yh2_y_nonreacting.png|250px]]
[[File:yo2_y_nonreacting.png|250px]]

'''Profile of mass fractions''' of <math>H_2</math> (left) and <math>O_2</math> (right) at <math>t = 2 \tau_{ref} ms</math>, <math>x = 0.5L</math>, and <math>z = 0.5L</math> for '''3-D non-reacting multi-species flow''' ('''Step 3''').

Regarding temperature, Figure 9 shows along the centerline '''two peaks''' and '''one valley''', as expected. Very small
deviations are revealed in the inlaid enlargements shown in Fig. 9.
Finally, the evolution with time of maximum temperature inside the computational domain is presented in Fig. 10.
Here again, no differences are observed at all concerning this parameter.
As a conclusion concerning this step, the three codes are able to reproduce numerically the behavior of a complex multi-species, non-isothermal flow with excellent agreement, and are thus strong candidates for high-fidelity
simulations of turbulent flames, as considered in the next and final step.