Volume I - Section V - CFD Methodology 
Page V - 11 
Note that the solution for each variable will depend on the solution for each and every variable in 
the neighboring cells and vice versa. The laws of physics based upon the conservation of mass, 
conservation of momentum, and conservation of energy must be preserved at all times. In this 
approach, turbulence is modeled using the established and robust two parameter method known 
as the k-epsilon model where k represents the kinetic energy and epsilon represents the rate of 
dissipation. 
The mathematical solution is highly iterative, with each iteration resulting in a set of errors. At 
the end of each iteration the errors for each variable are summed, normalized with an acceptable 
error, and plotted against iteration number (figure 5.03). A solution is reached when the sums of 
the errors for each, and all the variables, reaches a pre-determined and acceptable level. 
Each cell within the solution domain has eight equations associated with it: pressure, three 
velocities, temperature, two turbulence quantities, and concentration. An animal room model in 
this research typically has 100,000 to 600,000 cells, resulting in 4.8 to 6.4 million equations that 
have to be solved iteratively until the convergence criteria are satisfied. This extremely 
computer-intensive operation requires the use of powerful state-of-the-art workstations. 
Residual Error 
I EQ5 
1E04 
1 E05 
1 EQ2 
V 
& A 
|a\ 
tv'K 
i tv* N. 
V \ 
% 
O: 
■,\J 
s. 
1 E0I 
'''A'vW 
V \v- V 
v 
1 EQ0. 
... 
x 
101 201 301 401 SOI 
Repetition/Iteration No. 
601 
701 
Uariables 
Continuity 
K-uelocity 
V-uelocity 
Z-uelocity 
K.E. Turb. 
Oiss. Turb. 
Temperature 
Concentration 
Figure 5.03 Iterative Convergence History of a Simulation 
