Biomedical Engineering Reference
In-Depth Information
6.2.8 Numerical Considerations
6.2.8.1 Boundary Layer
The small thickness of the concentration boundary layer has consequences on the
numerical computation. It is essential to model precisely the mass transfer in the
boundary layer because it determines the mass transfer to the solid wall. To do so,
the computational grid needs to have at least two meshes in the boundary layer. It is
then necessary to reduce the side of the geometrical elements in the boundary layer,
especially where the boundary layer starts (Figure 6.14).
This reasoning often leads to very small values of the mesh size near the wall. A
mesh size of the order of a few microns is usual.
6.2.8.2 The Question of the Mesh Size
A numerical Peclet number is defined, associated to the size of the mesh
u x v y
D
D
æ
ö
P
=
max
,
(6.39)
ç
÷
em
è
ø
D
D
For the numerical calculation to be stable, the numerical Peclet number must
be smaller than 4
u x v y
D
D
æ
ö
P
=
max
,
<
4
(6.40)
ç
÷
em
è
ø
D
D
This condition requires the following limitations on the mesh size
4
D
D <
x
u
(6.41)
4
D
D <
y
v
Figure 6.14
Nonuniform computational grid at the vicinity of the wall, especially at the
beginning of the boundary layer.
