
ANSYS FLUENT uses a controlvolumebased technique to convert a general scalar transport equation to an algebraic equation that can be solved numerically. This control volume technique consists of integrating the transport equation about each control volume, yielding a discrete equation that expresses the conservation law on a controlvolume basis.
Discretization of the governing equations can be illustrated most easily by considering the unsteady conservation equation for transport of a scalar quantity . This is demonstrated by the following equation written in integral form for an arbitrary control volume as follows:
where  
=  density  
=  velocity vector (= in 2D)  
=  surface area vector  
=  diffusion coefficient for  
=  gradient of (= in 2D)  
=  source of per unit volume 
Equation 18.21 is applied to each control volume, or cell, in the computational domain. The twodimensional, triangular cell shown in Figure 18.2.1 is an example of such a control volume. Discretization of Equation 18.21 on a given cell yields
where  
=  number of faces enclosing cell  
=  value of convected through face  
=  mass flux through the face  
=  area of face , (= in 2D)  
=  gradient of at face  
=  cell volume 
Where is defined in Section 18.3.2. The equations solved by ANSYS FLUENT take the same general form as the one given above and apply readily to multidimensional, unstructured meshes composed of arbitrary polyhedra.