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In hypersonic flow computations, it is a key issue to predict surface heating accurately, though this is still challenging because there always are possibilities of resulting in anomalous solutions. In this paper, three properties for flux functions are proposed: 1) shock stability/robustness, 2) conservation of total enthalpy, and 3) resolving boundary layer. Then, numerical experiments are performed for widely used or recently developed flux functions, and these fluxes are categorized into five major groups based on how they satisfy the three properties. These tests reveal that no flux function investigated here possesses all the three properties. In particular, the first one is not satisfied by any flux functions, including flux-vector-splittings. Finally, contributions of those properties are compared in a two-dimensional, viscous, hypersonic blunt-body problem. Results showed that the first and the third properties are crucial, and the second one is preferred to predict hypersonic heating. A group of flux functions that best satisfies these properties is suggested, and they are recommended either to be used or designed for hypersonic heating computations.

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