Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-28T06:44:01.443Z Has data issue: false hasContentIssue false
  • English
  • Français

Solution of the Euler equations on unstructured grids for two-dimensional compressible flow

Published online by Cambridge University Press:  04 July 2016

L. Stolcis  and
L. J. Johnston
L. Stolcis
Affiliation:
Aeronautics/Aerospace Departmentvon Karman Institute for Fluid DynamicsRhode-St-Genese, Belgium
L. J. Johnston
Affiliation:
Aeronautics/Aerospace Departmentvon Karman Institute for Fluid DynamicsRhode-St-Genese, Belgium
Get access Rights & Permissions [Opens in a new window]

Abstract

A method for the numerical solution of the two-dimensional Euler equations on unstructured grids has been developed. The cell-centred symmetric finite-volume spatial discretisation is applied in a general formulation that allows the use of arbitrary polygonal computational cells. The integration in time, to a steady-state solution, is performed using an explicit, multi-stage procedure, with standard convergence acceleration techniques such as local time stepping, enthalpy damping and implicit residual smoothing. Accuracy of solution, in terms of minimising spurious entropy production, is achieved through careful treatment of the artificial dissipative terms near boundaries. Standard test cases for both subcritical and supercritical flows, including single- and multi-element aerofoils have been used to validate the method.

Type
Research Article
Information
The Aeronautical Journal , Volume 94 , Issue 936 , July 1990 , pp. 181 - 195
Copyright
Copyright © Royal Aeronautical Society 1990 

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.)

Footnotes

*

Present address: Department of Mechanical Engineering, UMIST, PO Box 88, Manchester M60 1QD

References

1. Deconinck, H. A survey of upwind principles for the multidimensional Euler equations, Von Karman Institute Lecture Series 1987–04, March 1987.Google Scholar
2. 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
3. Kroll, N. and Jain, R. K. Solution of Two Dimensional Euler Equations-Experience with a Finite Volume Code, DFVLR FB 87–41, 1987.Google Scholar
4. Weatherill, N. P. Mesh generation in CFD, Von Karman Institute Lecture Series, VKI-LS 1989–04, 6–10 March 1989.Google Scholar
5. Weatherill, N. P. A strategy for the use of hybrid structured-unstructured meshes in computational fluid dynamics, Proceedings of the 3rd Conference on Numerical Methods for Fluid Dynamics, Oxford, England, 21–24 March 1988, pp 101–116.Google Scholar
6. Weatherill, N. P., Johnston, L. J., Peace, A. J. and Shaw, J. A. A method for the solution of the Reynolds-averaged Navier-Stokes equations on triangular grids, Proceedings of the 7th GAMM Conference on Numerical Methods in Fluid Mechanics, Notes on Numerical Fluid Mechanics, Vol 20, pp 418–425, 1988, Vieweg, Braunschweig.Google Scholar
7. Jameson, A. Numerical solution of the Euler equations for compressible inviscid fluids, Numerical Methods for the Euler Equations of Fluid Dynamics, Angrand, F. et al, editors, 1985, pp 199–245, SIAM.Google Scholar
8. Jameson, A., Bakert, J. and Weatherill, N. P. Calculation of Inviscid Transonic Flow Over a Complete Aircraft, AIAA Paper 86–0103, 1986.Google Scholar
9. Mavriplis, D. and Jameson, A. Multigrid Solution of the Euler Equations on Unstructured and Adaptive Meshes, ICASE Report 87-53, July 1987 (also NASA CR 178346, 1987).Google Scholar
10. Mavriplis, D. Accurate Multigrid Solution of the Euler equations on Unstructured and Adaptive Meshes, AIAA Paper 88-3707, 1988.Google Scholar
11. Pulliam, T. H. Artificial Dissipation Models for the Euler Equations, AIAA Paper 85-0438, 1985.Google Scholar
12. Rizzi, A. Spurious Entropy Production and Very Accurate Solution to the Euler Equations, AIAA Paper 84-1644, 1984.Google Scholar
13. Jameson, A. and Baker, T. J. Multigrid Solution of the Euler Equations for Aircraft Configurations, AIAA Paper 84-0093, 1984.Google Scholar
14. Thomas, J. L. and Salas, M. D. Far-Field Boundary Conditions for Transonic Lifting Solutions to the Euler Equations, AIAA Paper 85-0020, 1985.Google Scholar
15. Rizzi, A. and Viviand, H. Numerical methods for the computation of inviscid transonic flows with shock waves, Notes on Numerical Fluid Mechanics, Volume 3, Vieweg, 1981.Google Scholar
16. Test Cases for Inviscid Flow Fields Methods, AGARD AR 211, 1985.Google Scholar
17. Weatherill, N. P. A method for generating irregular computational grids in multiply connected planar domains, Int J Numer Methods Fluids, 1988, 8, pp 181–197.Google Scholar
18. Suddhoo, A. and Hall, I. M. Test cases for the plane potential flow past multi-element aerofoils, Aeronaut J, December 1985, 89, (890), pp 403–414.Google Scholar
19. Williams, B. R. An Exact Test Case for the Plane Potential Flow About Two Adjacent Lifting Aerofoils, ARC R&M 3717, 1973.Google Scholar
20. Suddhoo, A. and Hall, I. M. Inviscid Compressible Flow Past a Multi-Element Aerofoil, AGARD CP 365, 1984.Google Scholar
21. Sinclair, P. M. An exact integral (field panel) method for the calculation of two-dimensional transonic potential flow around complex configurations, Aeronaut J, June/July 1986, 90, (896), pp 227–236.Google Scholar