Summary
The method of characteristics in space-time is used to solve the Navier-Stokes equations describing a hypersonic flow in the leading edge region of a circular cylinder. Because emphasis is put on the method, we assume laminar flow of a perfect gas in this paper. We proceed similarly as for unsteady and inviscid flows. First we transform the gas dynamic balance equations for viscous and heat-conducting gases from their non-conservative form into their characteristic form for establishing the compatibility conditions whose integral’s approximation leads to an explicit time-marching scheme for unsteady flows. Using a grid fitted between the bow shock and the surface of the body and starting from assumed approximate initial conditions and an assumed approximate initial position of the shock, a steady solution is then searched. This solution is compared with a solution of the method of characteristics for the inviscid case and with the solution for the viscous flow obtained by an implicit upwind finite volume method.
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Sanaknaki, H., Ballmann, J. (1999). A Numerical Simulation of a 2D- Viscous Hypersonic Flow Using the Time-Marching Method of Characteristics. In: Nitsche, W., Heinemann, HJ., Hilbig, R. (eds) New Results in Numerical and Experimental Fluid Mechanics II. Notes on Numerical Fluid Mechanics (NNFM), vol 72. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-10901-3_48
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DOI: https://doi.org/10.1007/978-3-663-10901-3_48
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
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