Volume I - Section V - CFD Methodology 
Page V - 23 
($p Qw) ~ D w {(f> P <p w ) (5.33) 
K 
Such that Dw is the west-face diffusion coefficient. There is a diffusion coefficient for each face 
of the cell. 
5.2. 5.2 Treatment of the convective terms 
The integration of the convective (sometimes referred to as advective) term is achieved by 
employing the upwind differencing scheme. Here, the value of the flow variable at a cell 
interface is equal to the flow variable on the upwind side of the face. Consider convection 
through the west face of the cell (where the fluid enters from the west neighboring cell): 
J ppU,.ndA = pU w AJ w = F w p w (5.34) 
Such that Fw is the west face convection coefficient. Again, there are convection coefficients for 
each face of the cell. 
By combining the effects of both convection and diffusion the finite volume equation is 
formulated: 
a p <p p = Yj a nn<i>nn+S (5.35) 
The coefficients ( ap etc.) that express the contribution of convection and diffusion across the cell 
boundaries are called matrix coefficients. Each matrix coefficient is simply the sum of both 
diffusion and convection coefficients. The value of the convection coefficient is determined by 
the direction from which fluid enters the cell. 
5.2.6 Solution of the Finite Volume Equations 
Having covered the derivation of all linearized equations from the governing partial differential 
equations, the process by which they are solved will now be explained. An iterative process is 
used, starting from an initial estimate of the values of all variables at each cell through to the 
converged solution where the final values obey their respective conservation equations to within 
an acceptable degree of accuracy. 
The solution process consists of two loops. An initial guess, or initial condition, is taken for the 
values of all variables at each cell. The two loops are then iterated in a nested manner. The inner 
