Accourding to the thought of TVD, we propose the TVD-type second-order CSCM^[1], from a siugle eqution, then extend it to system of equtions. To test the method and computer code, we compare our results for sphere with those of the reference [2]. Using our code, we simulate the supersonic viscous separated flow over indented nosetips. We compare the first-order results with the second-order results, and viscous results with inviscid results. Computational grids are generated by a simpler and faster quasi-orthogonal algebraic generation method.