In the numerical modelling of unsteady mixed subcritical and supercritical flows, a great simplification is attained when the algorithmic structure can be kept invariant during the whole course of the computation. This is commonly attained by reducing the influence of the convective momentum term when the flow approaches supercritical conditions, so as to maintain subcritical-like characteristic structures everywhere. The corresponding numerical scheme then becomes a flow-adaptive scheme. The consequences of using such a scheme are investigated and a variant of the momentum equation is identified which reduces the errors introduced through this process to an acceptable minimum.