An extension of Löhner (AIAA-93-3348-CP, 1993) for the generation of high aspect ratio volume grids on surfaces with ridges and corners is presented for Reynolds-averaged Navier–Stokes computations. Multiple point normals are introduced along ridges and corners. The original technique generates a semi-structured boundary layer of prismatic elements growing along point normals. Therefore, extra degenerated faces must be introduced to take into account the multiple growth curves at ridges and corners and produce a valid topological surface triangulation. The major task of the algorithm consists in recovering conformity in the surface mesh triangulation, which has been lost due to the introduction of the virtual faces. The procedure relies on a topological taxonomy of an arbitrary combination of concave and convex ridges. Each case is highlighted in detail. Special boundary conditions such as symmetry planes and periodic boundary conditions are also handled. Several complex geometries have been chosen to illustrate the proposed procedure, and timings are given, showing that the new module does not place any extra burden on the previous semi-structured approach. Copyright © 2008 John Wiley & Sons, Ltd.