A multi-dimensional time-marching method of characteristics for viscous and heat-conducting flows |
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Authors: | J Ballmann H Sanaknaki |
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Institution: | (1) Lehr- und Forschungsgebiet für Mechanik, RWTH Aachen Templergraben 64, D-52062 Aachen, Germany, DE |
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Abstract: | Summary A numerical scheme is presented which employs the characteristic surfaces in space-time for solving Navier-Stokes equations
for compressible fluid flow. We consider the general case of a three-dimensional flow, a simplification of which yields the
equations of the two-dimensional case. Emphasis is put on the method itself. We apply it to simulate a laminar hypersonic
flow around a circular cylinder of a five-components gas mixture of nitrogen and oxygen with thermally perfect constituents
and at chemical nonequilibrium. First, the partial differential equations are transformed into a standard form with directional
derivatives, enabling to attain the compatibility conditions, including the viscosity terms. These conditions are discretized
by approximating their integrals along the corresponding characteristic surfaces. The result is an explicit time-marching
numerical scheme. Using a grid fitted between the shock and the cylinder, and starting from roughly estimated initial conditions,
a steady solution is searched. A comparison is made with the solution obtained under the assumption of a perfect gas.
Received 6 April 1999; accepted for publication 13 May 1999 |
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Keywords: | Hypersonic flow method of characteristics viscous flow shock wave nonequilibrium flow |
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