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