FLOW AROUND A CYLINDER - istiarto

– 4.41 –
Wall function for the � equation. The turbulent kinetic-energy dissipation for cells
neighboring the wall is defined by Eq. 4.84. This can be easily implemented as follows:
� set all coefficients related to the neighboring cells to zero:
a E � a W � a N � a S � a T � a B � 0
� set the coefficient at cell P to unity: aP = 1
� set the source terms by (see Eq. 4.84):
c m�1 �
b � �P �
� �
3 4 m�1
kP
� � n,P
3 2
m�1
where kP is already computed in the previous step
(4.93)
Wall function and pressure correction. Since the discharge across the wall is zero, the
p
coefficient of the boundary node B in Eq. 4.68 is set to zero: aB � 0 . The pressure
correction at the boundary node is obtained by direct extrapolation from the cell center P:
c c
pB � pP .
4.5.5 Symmetry boundary
At the symmetry plane, for example at the east face (see Fig. 4.9), the convective
transport across the plane and the shear stress along the plane are zero. These properties
make the velocity at E be easily obtained from the projection of the velocity at P to the
plane. For the scalar variables, k and �, an approximation is used by extrapolating the
values at P to the boundary E. The following expressions thus apply at symmetry
boundaries:
Fig. 4.9 Symmetry boundary.