FLOW AROUND A CYLINDER - istiarto

– 4.33 –
� extrapolate all variables at P to E: � E � � P
�
�
� the outflowing discharge results:
��
qout � Ve
Pressure and velocity corrections
�Se � VP
�
� Se
The contribution of the discharge across the east face, q e , to the continuity equation, Eq.
4.66, is replaced by the outflowing discharge, q out . In forming the coefficients in Eq. 4.68,
the following steps are done:
p
� set the coefficient at node E to zero: aE � 0
� set the contribution of the inflowing discharge to the source term: b p
� � e � �q out
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
e c
� � ; this latter is obtained by the upwinding: p
E c � � � p
E c � � .
P
4.5.4 Wall boundary
Wall function approach
The wall function approach (Launder and Spalding, 1974) is applied to the cell whose
face is a rigid wall. Major assumptions used in this approach merit to be put forward
before presenting the derivation of the wall function; they are: (1) the no-slip flow
condition prevails at the wall with the universal logarithmic velocity distribution normal
to the wall, (2) the production of the turbulent kinetic energy is merely due to the
(turbulent) shear stress, thus neglecting the effect of the normal stress, and (3) a local
energy balance exists, i.e. the dissipation of the turbulent kinetic energy is equal to the
production. Given in the following paragraphs are the derivations of the wall function in
which those assumptions are further highlighted.