In the design of high speed vehicle, in order to ensure safety of flight, its surface pressure, density of heat flow distributions must be given accurately. Many computational schemes based on either the inviscid Euler equations or various forms of the Navier-Stokes equations can give out satisfied results in the predictions of pressure distributions. However computations of skin friction and in addition heat transfer particularly at high speeds have been a source of considerable difficulty. This paper adopts the finite volume method to solve the conservative type of Navier-Stokes equations simulating supersonic and hypersonic flow, for the aerodynamic heating problem. For the calculation of inviscous flow fluxes passing every surface element, the second order precision TVD scheme developed by Harten is adopted, the viscous flow fluxes are treated with centered differences of upwinded/downwinded averaged flow varibles. Numerical experiments show that the proposed schemes are quite robust and accurate.

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