AbstractA block relaxation scheme, grouped in a red‐black ordering, is applied to transonic aerofoil calculations using body‐fitted co‐ordinates. The scheme is simple and easily vectorizable. Detailed comparisons with the approximate factorization method (AF2) are presented and it is shown that the new scheme is competitive in all cases considered. Transonic results, of engineering accuracy, on an 0‐type grid of 149 × 30 points, are usually obtained within 200 iterations (≃ 40s on a