This paper presents a description and evaluation of a detailed mathematical simulation for the steady and unsteady flow in a radial inflow-turbine which is most frequently used, at present, for exhaust gas turbochargers of internal combustion engines. As a method of computation, the two-step differential Lax-Wendroff method and the characteristic method were used. The turbine characteristics, the mass flow rate, the power output and fluid movements at the turbine scroll inlet were compared with the experiment data. The results of the simulation were in good agreement with experimental values under both steady and unsteady flow conditions.