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Numerical solution of the unsteady navier-stokes equations in curvilinear coordinates: The hypersonic blunt body merged layer problem

  • Keith J. Victoria
  • George F. Widhopf
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 19)

Abstract

The Navier-Stokes solution of this study agrees with the Monte Carlo result in the shock layer region within the statistical scatter of the Monte Carlo calculation. Thus, it appears that the origin of the disagreement between the thin layer Navier-Stokes solution and the molecular simulation solution in the shock layer region is in the thin layer approximations and not in the Navier-Stokes stress-strain model and Fourier heat conduction law. It should be pointed out, however, that at this transitional flow condition (Kn = 0.10) the Monte Carlo solution shows that the temperature is not in equilibrium. Thus, for this particular flow condition, the molecular simulation technique is more appropriate.

The study also revealed interesting results regarding the numerical computation procedure in addition to the physical results. In particular, it was found that application of the leap-frog/Dufort-Frankel finite difference approximation to the continuity equation in curvilinear coordinates can lead to numerical instabilities. A simple time-averaging of the density in the inhomogeneous term in the continuity equation eliminated these instabilities. With this modification, it was possible to converge the numerical solution (cycle to cycle) for all flow variables to six significant figures.

Global conservation of mass, momentum and total energy can be accurately maintained with use of the non-conservative form of the Navier-Stokes equations. These quantities were found to be conserved to within one percent of their respective freestream inflow values.

Keywords

Shock Layer Hypersonic Flow Finite Difference Approximation Finite Difference Equation Stagnation Line 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • Keith J. Victoria
    • 1
  • George F. Widhopf
    • 1
  1. 1.The Aerospace CorporationLos Angeles

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