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A cartesian cut cell method for compressible flows Part A: static body problems

Published online by Cambridge University Press:  04 July 2016

G. Yang ,
D. M. Causon ,
D. M. Ingram ,
R. Saunders  and
P. Battent
G. Yang
Affiliation:
Centre for Mathematical Modelling and Flow Analysis, Manchester Metropolitan University, Manchester, UK
D. M. Causon
Affiliation:
Centre for Mathematical Modelling and Flow Analysis, Manchester Metropolitan University, Manchester, UK
D. M. Ingram
Affiliation:
Centre for Mathematical Modelling and Flow Analysis, Manchester Metropolitan University, Manchester, UK
R. Saunders
Affiliation:
Centre for Mathematical Modelling and Flow Analysis, Manchester Metropolitan University, Manchester, UK
P. Battent
Affiliation:
Centre for Mathematical Modelling and Flow Analysis, Manchester Metropolitan University, Manchester, UK
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Extract

A method for the calculation of steady or unsteady compressible flows is presented. The procedure, based on a cartesian cut cell approach and multi-dimensional high resolution upwind finite volume scheme, can cope with static or moving body problems having arbitrarily complex geometries. The method is described in two parts. In Part A, we discuss the cartesian cut cell approach and upwind finite volume scheme for static body problems. The method is validated on test problems involving both steady and unsteady compressible flows and then applied to some practical problems. The extension of the method to moving body problems is presented in Part B (pp 57-65).

Type
Research Article
Information
The Aeronautical Journal , Volume 101 , Issue 1002 , February 1997 , pp. 47 - 56
Copyright
Copyright © Royal Aeronautical Society 1997 

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Footnotes

†

Now at the Department of Engineering. UMIST.

References

1. Weatherill, N.P. and Forsey, C.R. Grid generation and flow calculations for complex aircraft geometries using a multi-block scheme, AIAA Paper 84-1665, 1984.Google Scholar
2. Steger, J.L., Dougherty, F.C. and Benek, J.A. A Chimera grid scheme, In: Advances in Grid Generation, ASME FED-5, 1983, pp 59–69.Google Scholar
3. Albone, C.M. Embedded meshes of controllable quality synthesised from elementary geometric features, AIAA Paper 92-0662, 1992.Google Scholar
4. Jameson, A., Baker, T.J. and Weatherill, N.P. Calculation of inviscid transonic flow over a complete aircraft, AIAA Paper 86-0103, 1986.Google Scholar
5. Peraire, J., Vahdati, M., Morgan, K. and Zienkiewicz, O.C. Adaptive remeshing for compressible flow computations, J Comp Phys, 1987, 72, pp 449–466.Google Scholar
6. Zeeuw, D.D. and Powell, K.G. An adaptively refined cartesian mesh solver for the Euler equations, J Comp Phys, 1993, 104, pp 56–68.Google Scholar
7. Berger, M.J. and LeVeque, R.J. An adaptive cartesian mesh algorithm for the Euler equations in arbitrary geometries, 1989, AIAA Paper 89- 1930.Google Scholar
8. Quirk, J.J. An alternative to unstructured grids for computing gas dynamic flows around arbitrarily complex two-dimensional bodies, Comp Fluids, 1994, 23, (1), pp 125–142.Google Scholar
9. Clarke, D.K., Salas, M.D. and Hassan, H.A. Euler calculations for multielement airfoils using cartesian grids, AIAA J, 1986, 24, (3).Google Scholar
10. Chiang, Y., van Leer, B. and Powell, K.G. Simulation of unsteady inviscid flow on an adaptively refined cartesian grid, AIAA Paper 92- 0443, 1992.Google Scholar
11. Coirier, W.J. and Powell, K.G. An accuracy assessment of cartesian mesh approaches for the Euler equations, AIAA Paper 93-3335, 1993.Google Scholar
12. van Leer, B. On die relation between die upwind-differencing schemes of Godunov, Engquist-Osher and Roe, SIAM J Scientific Stat Comp, 1984, 5.Google Scholar
13. Harten, A., Lax, P.D. and van Leer, B On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, SIAM Review, 1983, 25 (1), pp 35–61.Google Scholar
14. Toro, E.F., Spruce, M. and Speares, W. Restoration of me contact surface in the HLL Riemann solver, Shock Waves, 1994, 4, pp 25–34.Google Scholar
15. Batten, P., Lambert, C., Causon, D.M. and Clarke, N. On the choice of wavespeeds for HLL Riemann solvers, to appear in SIAM J Scientific Comp, November 1997.Google Scholar
16. Hentschel, R. and Hirschel, E.H. Self adaptive flow computations on structured grids, In: Proc of the Second ECCOMAS Computational Fluid Dynamics Conference, 1994, pp 243-249.Google Scholar
17. Woodard, P. and Colella, P. The numerical simulation of two-dimen sional fluid flow with strong shocks, J Comp Phys, 1984, 54, pp 115–173.Google Scholar
18. Jameson, A. and Mavriplis, D. Finite volume solution of me two-dimensional Euler equations on a regular triangular mesh, AIAA J, 1986, 24, (4), pp 611–618.Google Scholar
19. Bleakney, W., White, D. and Griffiths, W. Measurement of diffraction of Shockwave and resultant loading on structure, ASME J App Mech, 1950, 72, pp 439–445.Google Scholar
20. Mandella, M. and Bershader, D. Quantitative study of compressible vortices: generation, structure and interaction with airfoil, AIAA Paper 87-0328, 1987.Google Scholar
21. Yee, H.C. A class of high-resolution explicit and implicit shock-capturing methods, NASA TM 101088, February 1989.Google Scholar
22. Lohner, R. The efficient simulation of strongly unsteady flows by the finite element method, AIAA Paper 87-0555, 1987.Google Scholar