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

CHAPTER 4. NUMERICAL IMPLEMENTATION 61
The subgrid values are updated within the main iteration loop of the CFD
code. After 〈U〉, k, and ε or ω in the main grid have been updated in one
iteration, the subgrid update function is called. This function is essentially
the main iteration loop of another, embedded CFD code that performs one
iteration to solve for 〈U〉, k, and ˜ε or ω in the subgrid. Before the subgrid
calculations are performed, data are taken from the main grid to act as
boundary conditions on the subgrid. After the subgrid is updated, subgrid-
averaged values are extracted in order to act as wall function inputs to the
next main grid iteration. Thus, there is a cyclic exchange of information.
The data required as input to the subgrid calculation are the values of 〈U〉,
k, and ε or ω at the outer extent of the subgrid (where the subgrid ends and
the main grid transport equations begin). Transport equations are solved in
every subgrid cell (except in the case of the k-ω model, where the very-near-
wall values of ω are prescribed, as discussed above). At the wall node, zero
values of 〈U〉, k, and ˜ε are set. At the node placed farthest from the wall,
at the outer-most point on the subgrid, the values of 〈U〉, k, and ˜ε or ω are
set as being equal to the corresponding values linearly interpolated from the
two nearest main grid nodes.
The boundary conditions on the main grid are more complex. 〈U〉 receives its
boundary condition as in the above section on log-law wall functions, except
that the wall shear stress, τw is obtained from the application of Newton’s
law of viscosity at the subgrid’s near-wall cell node:
∂ 〈U〉
τw = ρν
∂y
y=0
Taking s1 as the near-wall subgrid cell node and discretising ∂〈U〉
∂y
y=0
(4.28)
within