A Total Variation Diminishing (TVD) scheme implemented in a non structured finite volume formulation for solving the 3D Euler equations is presented. To simultaneously, achieve adequate accuracy in smooth flows, high resolution at flow discontinuities and to avoid spurious oscillations, different flux limiter functions are applied in a wave-to-wave basis. By appropriately using compressive limiter functions with waves of the family two to four (linear waves), and diffusive limiter functions

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... waves of the family one and five (non linear waves), important reductions of the numerical viscosity can be achieved. This sort of adaptive scheme has satisfactorily been applied to the shock tube problem and to the slip interface between two parallel flows. It has also been used when computing the flow over a spherically blunted bi-conic body at free stream Mach numbers varying from five to fifteen. The results obtained with the blunted body are presented here, and they show that the new adaptive scheme besides being less diffusive, it does not lose robustness regarding other TVD methods.