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This work describes the thermochemical non-equilibrium simulations of reactive flow in twodimensions. The Van Leer and Liou and Steffen Jr. schemes, in their first-and second-order versions, are implemented to accomplish the numerical simulations. The Euler and Navier-Stokes equations, on a finite volume context and employing structured and unstructured spatial discretizations, are applied to solve the “hot gas” hypersonic flows around a blunt body, around a double ellipse, and around a reentry capsule in twodimensions. The second-order version of the Van Leer and Liou and Steffen Jr. schemes are obtained from a “MUSCL” extrapolation procedure in a context of structured spatial discretization. In the unstructured context, only first-order solutions are presented. The convergence process is accelerated to the steady state condition through a spatially variable time step procedure, which has proved effective gains in terms of computational acceleration (Maciel). The reactive simulations involve a Earth atmosphere chemical model of eleven species: