Abstract
A new high order accurate convection scheme, which satisfies TVD principle and is based on the non-linear functional relations between the normalised variables, has been developed. Applications of the scheme, together with QUICK and SMART, to the linear twodimensional passive scalar problems, indicate that both the proposed and SMART scheme return the most accurate and oscillation free solutions, in contrast over and undershoots were found in the QUICK's results. The scheme, which was implemented on both the density and pressure based solution algorithms, was further applied to one-dimensional unsteady compressible shock tube and steady nozzle flows. Predicted results which was contrasted with exact solutions, QUICK and SMART schemes, indicate the present methods returns the most accurate and least oscillatory results.