Page 219 - Finite Element Analysis with ANSYS Workbench

210 Chapter 11 Incompressible Flow Analysis

p cell
u cell

j  2
N
J  1

j  1 W staggered
grid
 y J P E
original
 y j grid
2 J  1
S
j  1
J  2 v cell

j  2
I  2 I  1 I I  1
i  2 i  1 i i  1 i  2
 x  x
2

11.2.1 Finite Volume Equations
With the concept of staggered grids, the u cell is moved
to the left of the p cell as shown in the figure. The new N, E, S and
W cells corresponding to this u cell are established. The velocity u
is then determined from,
u
au  u P P  au nb  ( p I 1,J  p , I J ) A
u
nb
u
where A is the flow area on the left and right edges of the cell.
The subscript nb means the neighbor cells of the u cell.
Similarly, the velocity v is determined from,
av  v PP  av  ( p , I 1J   p , I J ) A
v
v
nb nb
v
where A is the flow area on the top and bottom edges of the cell.
The coefficients a and a in the equations above
P
nb
consist of the convection and diffusion terms of the p cell. These