
FLUENT uses a controlvolumebased technique to convert the governing equations to algebraic equations that can be solved numerically. This control volume technique consists of integrating the governing equations about each control volume, yielding discrete equations that conserve each quantity on a controlvolume basis.
Discretization of the governing equations can be illustrated most easily by considering the steadystate 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 24.21 is applied to each control volume, or cell, in the computational domain. The twodimensional, triangular cell shown in Figure 24.2.1 is an example of such a control volume. Discretization of Equation 24.21 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)  
=  magnitude of normal to face  
=  cell volume 
The equations solved by FLUENT take the same general form as the one given above and apply readily to multidimensional, unstructured meshes composed of arbitrary polyhedra.
By default, FLUENT stores discrete values of the scalar at the cell centers ( and in Figure 24.2.1). However, face values are required for the convection terms in Equation 24.22 and must be interpolated from the cell center values. This is accomplished using an upwind scheme.
Upwinding means that the face value is derived from quantities in the cell upstream, or ``upwind,'' relative to the direction of the normal velocity in Equation 24.22. FLUENT allows you to choose from several upwind schemes: firstorder upwind, secondorder upwind, power law, and QUICK. These schemes are described in Sections 24.2.1 24.2.4.
The diffusion terms in Equation 24.22 are centraldifferenced and are always secondorder accurate.