AbstractSpatial operators used in unstructured finite volume flow solvers are analysed for accuracy using Taylor series expansion and Fourier analysis. While approaching second‐order accuracy on very regular grids, operators in common use are shown to have errors resulting in accuracy of only first‐, zeroth‐ or even negative‐order on three‐dimensional tetrahedral meshes. A technique using least‐squares optimization is developed to design improved operators on arbitrary meshes. This is applied to the fourth‐order edge sum smoothing operator. The improved numerical dissipation leads to a much more accurate prediction of the Strouhal number for two‐dimensional flow around a cylinder and a reduction of a factor of three in the loss coefficient for inviscid flow over a three‐dimensional hump. Copyright © 2001 John Wiley & Sons, Ltd.