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Local grid refinement aims to optimise the relationship between accuracy ofthe results and number of grid nodes. In the context of the finite volumemethod no single local refinement criterion has been globally established asoptimum for the selection of the control volumes to subdivide, since it is noteasy to associate the discretisation error with an easily computable quantityin each control volume. Often the grid refinement criterion is based on anestimate of the truncation error in each control volume, because the truncationerror is a natural measure of the discrepancy between the algebraicfinite-volume equations and the original differential equations. However, it isnot a straightforward task to associate the truncation error with the optimumgrid density because of the complexity of the relationship between truncationand discretisation errors. In the present work several criteria based on atruncation error estimate are tested and compared on a regularised lid-drivencavity case at various Reynolds numbers. It is shown that criteria where thetruncation error is weighted by the volume of the grid cells perform betterthan using just the truncation error as the criterion. Also it is observed thatthe efficiency of local refinement increases with the Reynolds number. Thetruncation error is estimated by restricting the solution to a coarser grid andapplying the coarse grid discrete operator. The complication that hightruncation error develops at grid level interfaces is also investigated andseveral treatments are tested.

Numerical experiments on the efficiency of local grid refinement based on truncation error estimates