  Explicit non-oscillatory central difference schemes become excessively
diffusive when applied to highly nonlinear advection problems where small time
steps are necessary to maintain stability. Here, we present a correction to
reduce such numerical dissipation for this class of problems. The correction is
obtained by selecting the appropriate finite difference approximations for
calculating the slopes utilized to reconstruct the solution from the cell
averages. The anti-diffusive central scheme does not require any knowledge of
the eigenstructure and is fully central. The proposed correction is applied to
the widely used Nessyahu-Tadmor scheme to demonstrate the utility of the
correction. The stability of the corrected scheme is discussed and the
condition for the scheme to become TVD (total variation diminishing) is
presented. The corrected scheme is finally tested with a number of test cases
and the results are compared with analytical solutions and published results
showing the ability of the corrected scheme to effectively resolve sharp
discontinuities.
