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

CHAPTER 5. RESULTS 81
maxima). This is particularly visible in Figure 5.31, but Figure 5.27 shows
that the local minimum between these two peaks lies at y/δ = 0.2, the limit
of the subgrid region and also the point where boundary conditions from the
subgrid are applied to the main grid and visa versa. Close inspection of all
the k + profiles produced by the k-ω subgrid reveals minor discontinuities at
this y/δ location for other phase angles also. This is a result of the way
in which the subgrid solution of ω was applied as a boundary condition to
the main grid. The UMIST-N approach to k and ε boundary conditions
is to calculate subgrid averaged production and dissipation terms for these
parameters, which are then applied as source terms within the near-wall cell
in the main grid solution. However, ω tends to infinity at the wall, and
source terms on ω become numerically unwieldy in near-wall cells. Thus,
subgrid averaged production of ω could not be obtained and instead the
subgrid profile of ω was interpolated to the main grid node and applied there
as a fixed value. 2 This boundary condition appears to be less effective than
the average source approach, and, until a more satisfactory solution to the ω
boundary condition problem can be found, it advises against the applicability
of the UMIST-N approach to a k-ω model solution. This aside, the subgrid
k-ω results appear satisfactory when considered as a whole.
In addition to the above difficulty in the prescription of an ω boundary
condition, further difficulties were encountered in attempting to run the k-ω
model in the subgrid with a high-Reynolds-number k-ε model in the main
grid. Poor results were seen to arise from the difference in the values of k
produced by the two models under similar conditions. In general, the k-
ω model produces lower values of k than the k-ε model, as noted in the
2 See Chapter 4 for more information.