AbstractAdaptive refinement is implemented in the context of the volume‐of‐fluid (VOF) methodology in order to study the efficacy of resolving interfaces adaptively based on the local value of curvature. The usual uniform mesh VOF implementation is modified slightly to ensure accurate advection of fluxes between cells at different resolutions. Normals and curvatures are calculated accurately via height functions. Results of a series of tests indicate that in most instances the use of adaptive refinement (when compared to uniform refinement with a similar number of cells) leads to more accurate VOF advection. The results also clearly show that curvature‐based adaptive refinement leads to a distribution of errors along an interface that is nearly independent of curvature. Copyright © 2007 John Wiley & Sons, Ltd.