Volume I - Section V - CFD Methodology 
Page V - 9 
2) Numerically Solving the Physical Model 
Integration is one of the cornerstones of calculus, the other being differentiation. In order to find 
the solution domain (the area under a solution curve) numerically, the curve would be chopped 
up into little pieces, and then the area under each little curve would be approximated. The sum of 
all of the approximate little areas would be close to the actual area under the curve. The 
difference between the actual and approximate areas is the numerical error. The object is to make 
this error so small it is not noticeable. In CFD, rather than integrating a relatively simple function 
like the equation for a curve, the governing equations of motion for a fluid continuum are 
integrated. 
Let us consider a typical animal facility. The objective is to predict airflow, temperature, and 
concentration of any airborne contaminant at any point in the room space. 
Figure 5.01 shows a set of design parameters such as 
• the geometry and layout of the animal room 
• the sources of heat and contaminants, 
• as well as the position of exhaust and ventilation systems. 
In order to do this, the three-dimensional space of the animal room is subdivided into a large 
number of control volume cells (figure 5.02). The size of the cells influences the detail and 
accuracy of the final results. In all the whole animal room cases, the number of grid cells ran into 
the hundreds of thousands, and, in some instances, totaled over one million grid cells. 
The equations in each cell represent the mathematical definition of the equipment and 
phenomena contained within it. For example, a cell could encompass a volume that envelops the 
following: 
• a representation of a group of mice 
• or some heat source 
• or just some air. 
The CFD software will then attempt to solve the Navier-Stokes equation for a predetermined set 
of variables for each cell. In a typical three-dimensional calculation these variables would 
represent the following: 
• velocities in three directions, 
• temperature, 
• pressure, 
• concentration, 
• and the turbulence quantities. 
