FLOW AROUND A CYLINDER - istiarto

– 4.31 –
The above relation holds as well for p � and p c values.
The boundary node denoted by W (instead of w) upon which the inflow boundary values
are defined allows the discretized equations formerly established for interior nodes to be
applied to the boundary node W without the need to change the notation.
Momentum and k-� equations
Fig. 4.6 Inflow boundary.
In forming the coefficients in Eq. 4.52, the following steps apply:
� all variables at the inlet are given: � W � � in
� evaluate the convective-diffusive terms as for normal interior cells:
C D C D
aW, a W,
aP
� � , �a W P�
, b
W D � � , b
W 1D � � , b
W 2D � �W � bring the contribution of node W to the source term: b � b � b D
� set the coefficient at node W to zero: a W � 0
Pressure and velocity corrections
� � W � a W
C D � � a W��
W
The contribution of the discharge across the west face, q w , to the continuity equation, Eq.
4.66, is replaced by the imposed discharge, q in . In forming the coefficients in Eq. 4.68,
the following steps apply:
p
� set the coefficient at node W to zero: aW � 0
� set the contribution of the inflowing discharge to the source term: b p
� � w � �q in
For the velocity correction, Eq. 4.57, the pressure correction gradient, �p c �x i , is
computed by the finite-volume technique, Eq. 4.20, which requires the value of
p c � � � p
w c
� � W . This latter is obtained by Eq. 4.73.