AbstractA numerical scheme is presented for the solution of the Euler equations of compressible flow of a gas in a single spatial co‐ordinate. This includes flow in a duct of variable cross‐section as well as flow with slab, cylindrical or spherical symmetry and can prove useful when testing codes for the two‐dimensional equations governing compressible flow of a gas. The resulting scheme requires an average of the flow variables across the interface between cells and for computational efficiency this average is chosen to be the arithmetic mean, which is in contrast to the usual ‘square root’ averages found in this type of scheme. The scheme is applied with success to five problems with either slab or cylindrical symmetry and a comparison is made in the cylindrical case with results from a two‐dimensional problem with