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The reduction of numerical entropy generated by unsteady Shockwaves

Published online by Cambridge University Press:  04 July 2016

C. B. Allen
C. B. Allen*
Affiliation:
Department of Aerospace EngineeringUniversity of BristolBristol, UK
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Abstract

The computation of slowly moving Shockwaves is considered. A numerical error is introduced into the solution during an explicit computation, which results in the generation of spurious entropy. The generation of this spurious entropy and its effect on the pressure wave in Euler flows is examined, in one dimension by considering a moving shock in a constant area duct, and in two dimensions by considering an unsteady aerofoil flow. An efficient temporal discretisation is presented, whose advantages over the explicit scheme are two-fold. First, the numerical entropy generation due to shock motion is eliminated, and second, the CPU requirements for a two-dimensional unsteady computation are reduced by a factor of five from that required for the explicit scheme, for no loss of accuracy.

Information

Type
Research Article
Information
The Aeronautical Journal , Volume 101 , Issue 1001 , January 1997, pp. 9 - 16
Copyright
Copyright © Royal Aeronautical Society 1997 

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References

1. Woodward, P. and Collela, P. The numerical simulation of two- dimensional fluid flow through shocks, J Comp Phys, 54, (1), 1984, pp 115–173.Google Scholar
2. Roberts, T.W. The behaviour of flux-difference splitting schemes near slowly moving Shockwaves, J Comp Phys, 90, (1), 1990, pp 141–160.Google Scholar
3. Lindquist, D.R. and Giles, M.B. On the validity of linearized unsteady Euler equations with shock capturing, AIAA Paper 91-1598, June 1991.Google Scholar
4. Meadows, K.R., Cauohey, D.A. and Casper, J. Computing unsteady Shockwaves for aeroacoustic applications, AIAA J, 32, (7), 1994, pp 1360–1366.Google Scholar
5. Van-Leer, B. Flux-vector splitting for the Euler equations, Lecture Notes in Physics, 170, 1982, pp 507–512.Google Scholar
6. Jameson, A. Time dependent calculations using multigrid, with applica tions to unsteady flows past airfoils and wings, AIAA Paper 91-1596, June 1991.Google Scholar
7. Anderson, W.K., Thomas, J.L. and Van-Leer, B. Comparison of finite volume flux vector splittings for the Euler equations, AIAA J, September 1986, 24, pp 1453–1460.Google Scholar
8. Jameson, A., Schmidt, W. and Turkel, E. Numerical solution of the Euler equations by finite-volume methods using Runge-Kutta time- stepping schemes, AIAA Paper 81-1259, 1981.Google Scholar
9. Turkel, E. and Van-Leer, B. Runge-Kutta Methods for Partial Differential Equations, ICASE Report, 1983.Google Scholar
10. Pike, J. Exact Analytic Solutions for Viscous Shock-Waves with Implications for numerically Captured Shock-Waves, RAE Technical Report 85041, 1985.Google Scholar
11. Parpia, I.H. Van-Leer flux-vector splitting in moving coordinates, AIAA J, January 1988, 26, pp 113–115.Google Scholar
12. Thomas, P.D. and Lombard, C.K. Geometric Conservation Law and its application to flow computations on moving grids AIAA J, October 1979, 17, pp 1030–1037.Google Scholar
13. Gordon, W.J. and Hall, C.A. Construction of curvilinear coordinate systems and applications of mesh generation, Int J Num Methods Eng, 1973, 7, pp 461–477.Google Scholar
14. Eriksson, L.E. Generation of boundary-conforming grids around wing- body configurations using transfinite interpolation, AIAA J, 1982, 20, (10), pp 1313–1320.Google Scholar
15. Allen, C.B. Central-difference and upwind-biased schemes for steady and unsteady Euler aerofoil computations, Aeronaut J, 1995, 99, (982), pp 52–62.Google Scholar
16.(Anonymous) Compendium of unsteady aerodynamic measurements, AGARD-R-702, 1982.Google Scholar