For incompressible flow the mass flow as expressed by Equation (667) can be written as:
![]() |
(762) |
where
is a function of
only. Therefore, the density is constant while treating the mass
conservation equation. Using Equation (662) this can be further
rewritten as:
In the next step Equation (661) is approximated by:
![]() |
(764) |
Notice that
in the
-term was replaced
by
. This does not correspond to the SIMPLE algorithm, since
the term is not neglected, but also not quite corresponds to the SIMPLEC
algorithm, since
is used. Writing this equation for the
neighboring element E and taking the mean leads to:
![]() |
(765) |
in which the second order correction
was used. Therefore
Equation (763) now reduces to:
![]() |
(766) |
or, with the abbreviation
:
![]() |
(767) |
If the velocity on the face is known the mass flow can be calculated directly. Therefore, Equation (677) now reads:
![]() |
(768) |
where stands for the faces on which the velocity is defined by the
user. Notice that the unknown here is the pressure and not the correction to
the pressure as in compressible flow.
The pressure gradient can be treated as in Equation (679). Alternatively, one can also write (Figure 173):
![]() |
(769) |
Since
![]() |
(770) |
and
![]() |
(771) |
one obtains:
![]() |
(772) |
If the pressure is known on the face, the expression reduces to:
![]() |
(773) |