The philosophy of time-marching method is firstly applied to through-flow computation.The governing equation is solved with four step Runge-Kutta scheme.In result

the difficulty in the transonic highly-loaded turbomachinery designing

is surmounted.As an example

an axial supersonic inflow shock rotor is designed

with a fine grid

a strong shock is found in flow path.It is indicated that the time-marching method is suitable for through-flow calculation

especially for turbomachinery

whose flow velocity axial component is transonic.