  Local grid refinement aims to optimise the relationship between accuracy of
the results and number of grid nodes. In the context of the finite volume
method no single local refinement criterion has been globally established as
optimum for the selection of the control volumes to subdivide, since it is not
easy to associate the discretisation error with an easily computable quantity
in each control volume. Often the grid refinement criterion is based on an
estimate of the truncation error in each control volume, because the truncation
error is a natural measure of the discrepancy between the algebraic
finite-volume equations and the original differential equations. However, it is
not a straightforward task to associate the truncation error with the optimum
grid density because of the complexity of the relationship between truncation
and discretisation errors. In the present work several criteria based on a
truncation error estimate are tested and compared on a regularised lid-driven
cavity case at various Reynolds numbers. It is shown that criteria where the
truncation error is weighted by the volume of the grid cells perform better
than using just the truncation error as the criterion. Also it is observed that
the efficiency of local refinement increases with the Reynolds number. The
truncation error is estimated by restricting the solution to a coarser grid and
applying the coarse grid discrete operator. The complication that high
truncation error develops at grid level interfaces is also investigated and
several treatments are tested.
