Abstract: Referring to the construction way of Lax-Wendroff scheme, new IRS(Implicit Residual Smoothing) schemes have been developed for hyperbolic, parabolic and hyper-parabolic equations. These IRS schemes have 2nd-order or 3rd-order time accuracy, and can extend the stability region of basic explicit time-stepping scheme greatly and thus can permit higher CFL number in the calculation of flow field. The central smoothing and upwind-bias smoothing techniques have been developed too. Based on one-dimensional linear model equation, it has been found that the scheme is unconditionally stable according to the von-Neumann analysis. The limitation of Dawes’ method, which has been applied in turbomachinery widespreadly, has been discussed on solving steady flow and viscous flow. It is shown that stable solution of this method is not completely independent with the value of time step. In the end, numerical results by using IRS schemes and Dawes’ method as well as TVD (total variation diminishing) scheme and four-stage Runge-Kutta technique are presented to verify the analytical conclusions.

Key words: IRS scheme, four-stage Runge-Kutta technique, TVD scheme