4.2 Approximation of Surface Integrals
73
l i
x
xi.^
Xi
xi+^
Fig. 4.2. A typical CV and the notation used for a Cartesian 2D grid
Fig. 4.3. A typical CV and the notation used for a Cartesian 3D grid
In what follows, only a typical CV face, the one labeled 'e' in Fig. 4.2 will
be considered; analogous expressions may be derived for all faces by making
appropriate index substitutions.
To calculate the surface integral in Eq. (4.2) exactly, one would need
to know the integrand f everywhere on the surface S, . This information is
not available, as only the nodal (CV center) values of 4 are calculated so
an approximation must be introduced. This is best done using two levels of
approximation:
the integral is approximated in terms of the variable values at one or more
locations on the cell face;