An efficient method for achieving the non‐uniform grids on a spherical geometry is presented here. It uses the icosahedral–hexagonal grid with successive refinement to arrive at the target grid suitable for computational fluid dynamics (CFD) applications. It reduces the complexity of search from O(n2) to O(n) on icosahedral–hexagonal grids where n refers to the refinement level. The numerical solution of the transport equation is performed using the initial conditions of a well‐known problem (solid‐body rotation); the numerical scheme is second‐order accurate. Since advection of chemically active tracers in the atmosphere and their modelling are becoming a major area of concern within the climate change scenario, this study assures the efficiency and accuracy of the numerical scheme as tested here for tracer transport. Copyright © 2010 Curtin University of Technology and John Wiley & Sons, Ltd.