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A Total Variation Diminishing (TVD) MacCormack scheme is used to study the three-dimensional separation at wing/body junctions in supersonic flows. The new scheme is robust, resolves discontinuities well without any numerical oscillations present in the flow field. Moreover, this new scheme does not contain any problem dependent parameters to be adjusted and many production codes employing MacCormack algorithm can be easily updated to good effect. Numerical simulation carried out in laminar supersonic junction flows using the new scheme yields improved prediction for the separation location and the axial velocity profiles in the separated flow region.