Abstract: The objective of this paper is to review and assess time marching method used for the analysis and design of turbomachinery. There are two classes of methods for solving the time-dependent equations:explicit and implicit. In these methods, the time derivatives in the Euler/Navier-Stokes equations are retained, thus making the equations hyperbolic in nature. Very efficient techniques have been developed to solve these hyperbolic equations for the internal flow fields of turbomachinetry. The emphasis of thi...