How to multi-stage a simple numerical scheme (e.g. FORCE). The Riemann problem is solved for several time steps using the simple scheme on the two-cell domain, with transmissive boundary conditions as shown by the empty arrows. The solid lines show the wave structure of the solution. As the number of stages increases, the waves move away from the centre, so that the flux at the centre tends to the correct limit, which is represented by the filled arrow at the top. This figure corresponds to calculating the FORCE³ scheme, if FORCE is used as the underlying simple scheme.