Abstract
A new adaptive high-order-accurate convection scheme that satisfies the unsteady total variation diminishing principle has been developed. The second-order accuracy of the proposed scheme was verified by numerical experiments on the unsteady linear and nonlinear scalar equations. The new scheme was further applied to one-dimensional unsteady compressible shock tube and steady nozzle flows and a two-dimensional shock reflection problem. Predicted results indicate that the present method returns a high order of accuracy and oscillation free results.