In two-or three-dimensional flow fields

it is difficult to determine the direction of wave propagation in cascades due to complexity of transonic flow.Now a grid-independent approximate Riemann solver is applied to numerical simulation of two-dimensional transonic cascade flow by the Euler or Navier-Stokes equations.Fluxes on grid faces are obtained via wave decomposition

assuming that information propagates in the velocity difference directions

rather than in the grid-normal directions as in a standard grid-aligned solver.Second-order computations with the grid-independent flux function are used to analyze two typical examples of transonic cascades.The results indicate that the grid-independent model suppresses entropy production over the cascade surface due to either computational diffusion or grid viscosity

and resolves shock and shear waves in transonic flow of cascades much better.