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

CHAPTER 4. NUMERICAL IMPLEMENTATION 64
about by the way in which main grid and subgrid solutions are updated in
alternation, with data from each being passed as boundary conditions to the
other, in turn. Finally, the subgrid allows a very different level of grid re-
finement to be employed within the subgrid than in the main grid. Thus,
extensive near-wall grid refinement may be achieved without the numerical
problems that are usually associated with a single grid employing a very large
expansion factor.
4.5 Under-Relaxation
Under-relaxation is a technique that involves hindering the rate of conver-
gence of the CFD code in order to dampen spurious effects and reduce the
risk of overshooting the converged solution.
Generally, after an updated solution to one of the governing differential equa-
tions has been obtained, the resulting calculated local values of a quantity φ
will replace the previous values, according to
φ new = φ calc
(4.34)
When under-relaxation is used, an under-relaxation factor, α may be applied,
and the updated values of φ will be the weighted average of φ calc and φ old ,
according to
φ new = αφ calc + (1 − α) φ old
(4.35)