Hostname: page-component-7479d7b7d-68ccn Total loading time: 0 Render date: 2024-07-15T21:00:22.556Z Has data issue: false hasContentIssue false
  • English
  • Français

The solution of the Navier-Stokes equations for two-dimensional compressible flows using a simple second order accurate algorithm

Published online by Cambridge University Press:  04 July 2016

K. P. Sinhamahapatra
K. P. Sinhamahapatra*
Affiliation:
Aerospace Engineering Department, Indian Institute of Technology, Kharagpur
Get access Rights & Permissions [Opens in a new window]

Summary

The compressible flow Navier-Stokes equations, in conservation form, have been solved using a modified MacCormack implicit predictor-corrector scheme. For turbulent flow the solution is modified by incorporating an eddy viscosity, to solve the Reynolds-averaged Navier-Stokes equations. The algorithm is accurate to second order in time and space and is unconditionally stable. It requires the solution of block bidiagonal matrices and the programme can run on commonly available minicomputers. It also has the advantage that a steady state solution is approached, if it exists, independent of the time step employed.

Numerical results are presented for the two-dimensional shock-boundary layer interaction in both laminar and turbulent flow and the results are compared with experimental values and the numerical results of other workers. The method is calibrated against the analytical solution for the boundary layer on a flat plate and for the time dependent Couette flow problem.

Type
Research Article
Information
The Aeronautical Journal , Volume 97 , Issue 964 , April 1993 , pp. 131 - 137
Copyright
Copyright © Royal Aeronautical Society 1993 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Peyret, R. and Viviand, H. Computation of viscous compressible flows based on the Navier-Stokes equations, AGARD AG-212 (1975).Google Scholar
2. Anderson, D.A., Tannehill, J. C. and Pletcher, R.H. Computational Fluid Mechanics and Heat Transfer, Hemisphere Publishing, New York, 1984.Google Scholar
3. Maccormack, R.W. A numerical method for solving the equations of compressible viscous flow, AIAA J, September 1982, 19, (9), pp 1275–1281.Google Scholar
4. Cebeci, T. and Smith, A.M.O. Analysis of Turbulent Boundary Layers, Academic Press, New York, 1974.Google Scholar
5. Schlichting, H. Boundary Layer Theory, Pergamon Press, New York, 1955.Google Scholar
6. White, F.M. Viscous Fluid Flow, McGraw-Hill, New York, 1974.Google Scholar
7. Pappas, C.C. Measurement of Heat Transfer in the turbulent boundary layer on a flat plate in supersonic flow and comparison with skin friction results, NACA TN 3222, 1954.Google Scholar
8. Hakkinen, R.J., Greber, L., Trilling, L. and Abarbanel, S.S. The interaction of an oblique shock wave with a laminar boundary layer, NASA Memorandum 2-18-59W, 1959.Google Scholar
9. Beam, R.M. and Warming, R.F. An implicit factored scheme for the compressible Navier-Stokes Equations, AIAA J, April 1978, 16, (4).Google Scholar
10. Viegas, J.R. and Horstman, C.C. Comparison of multiequation turbulence models for several shock separated boundary layer interaction flows, AIAA Paper 78-1165, July 1978.Google Scholar
11. Jones, W.P. and Launder, B.E. The prediction of laminarization with a two-equation model of turbulence, Intl J Heat Mass Trans, February 1972, 15.Google Scholar