Abstract: In the present paper a number of TVD schemes are tested and compdred throughamodel equation。 Numerical results show that Some schelnes are more “compressive”andsome are more“diffusive”.To avoid the“overcompressibility” and“overdiffusion”, a newkind of TVD scheme is proposed.It is constructed in the hybrid form of a more compressiveTVD scheme and a more diffusive TVD scheme 。 With the introduction of an adaptiveweighted function,the new scheme maintains high resolution in sharp discontinuities andaVoids“o...