The UMIST-N Near-Wall Treatment Applied to Periodic Channel Flow

CHAPTER 4. NUMERICAL IMPLEMENTATION 63
Unfortunately, a similar approach was found to be impossible in specifying
the boundary condition on ω. This is thought to be due to the near-wall be-
haviour of ω. Because ω approaches infinity near the wall, subgrid-averaged
production and destruction values are difficult to obtain. Therefore, ω is
specified at the main grid near-wall cell node according to linear interpola-
tion between the two closest subgrid nodes. Given an interpolated subgrid
ω value, ωsg, the source terms on ω in the main grid are
where G is a large number.
SP = −G
SU = G · (ωsg) (4.33)
The UMIST-N subgrid wall function simplifies near-wall calculation, as com-
pared to a low-Reynolds-number treatment, by removing pressure correction
and the wall-normal momentum equation from the solution procedure. Thus,
the flow calculation is reduced to a parabolic problem. Since PASSABLE
is a parabolic code with wall-normal velocity constrained to be zero, the
differences between the subgrid wall function approach and a low-Reynolds-
number treatment of steady channel flow may be expected to be less sig-
nificant, both in terms of accuracy and computational cost, than would be
found in other flow geometries.
One key difference remaining between the subgrid and low-Reynolds-number
calculations is the necessity of applying subgrid results to the main grid as
wall-function-type boundary conditions, rather than solving the governing
equations in an uninterrupted manner through the near-wall region. Fur-
thermore, a potential exists for instability to be introduced by the lag that
exists between a main grid update and a subgrid update. This lag comes