Abstract
A new adaptive high-order-accurate convection scheme, which satisfies the unsteady TVD principle has been developed. Applications of the scheme, together with QUICK,. bounded-QUICK and second order upwind scheme, to linear two-dimensional passive scalar problems, indicate that both the proposed scheme and the bounded-QUICK scheme return the most accurate and oscillation-free solutions; by contrast, overshoots and undershoots were found in the QUICK and second-order upwind scheme results. In the unsteady wave equation, the proposed scheme was found to produce the most accurate results. The new scheme was further applied to one-dimensional unsteady compressible shock tube and steady nozzle flows and two-dimensional shock reflection problem. Predicted results indicate that the present method returns the most accurate and least oscillatory results.