Aerodynamic Computations Using a Finite Volume Method with an HLLC Numerical Flux Function
Mathematical modelling of natural phenomena, Tome 6 (2011) no. 3, pp. 189-212.

Voir la notice de l'article provenant de la source EDP Sciences

A finite volume method for the simulation of compressible aerodynamic flows is described. Stabilisation and shock capturing is achieved by the use of an HLLC consistent numerical flux function, with acoustic wave improvement. The method is implemented on an unstructured hybrid mesh in three dimensions. A solution of higher order accuracy is obtained by reconstruction, using an iteratively corrected least squares process, and by a new limiting procedure. The numerical performance of the complete approach is demonstrated by considering its application to the simulation of steady turbulent transonic flow over an ONERA M6 wing and to a steady inviscid supersonic flow over a modern military aircraft configuration.
DOI : 10.1051/mmnp/20116308

L. Remaki 1 ; O. Hassan 1 ; K. Morgan 1

1 School of Engineering, Swansea University, Swansea SA2 8PP, Wales, UK
@article{MMNP_2011_6_3_a8,
     author = {L. Remaki and O. Hassan and K. Morgan},
     title = {Aerodynamic {Computations} {Using} a {Finite} {Volume} {Method} with an {HLLC} {Numerical} {Flux} {Function}},
     journal = {Mathematical modelling of natural phenomena},
     pages = {189--212},
     publisher = {mathdoc},
     volume = {6},
     number = {3},
     year = {2011},
     doi = {10.1051/mmnp/20116308},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20116308/}
}
TY  - JOUR
AU  - L. Remaki
AU  - O. Hassan
AU  - K. Morgan
TI  - Aerodynamic Computations Using a Finite Volume Method with an HLLC Numerical Flux Function
JO  - Mathematical modelling of natural phenomena
PY  - 2011
SP  - 189
EP  - 212
VL  - 6
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20116308/
DO  - 10.1051/mmnp/20116308
LA  - en
ID  - MMNP_2011_6_3_a8
ER  - 
%0 Journal Article
%A L. Remaki
%A O. Hassan
%A K. Morgan
%T Aerodynamic Computations Using a Finite Volume Method with an HLLC Numerical Flux Function
%J Mathematical modelling of natural phenomena
%D 2011
%P 189-212
%V 6
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20116308/
%R 10.1051/mmnp/20116308
%G en
%F MMNP_2011_6_3_a8
L. Remaki; O. Hassan; K. Morgan. Aerodynamic Computations Using a Finite Volume Method with an HLLC Numerical Flux Function. Mathematical modelling of natural phenomena, Tome 6 (2011) no. 3, pp. 189-212. doi : 10.1051/mmnp/20116308. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20116308/

[1] T. Barth. A 3–D upwind Euler solver for unstructured meshes. AIAA–91–1548–CP, 1991.

[2] T. Barth, D. Jespersen. The design and application of upwind schemes on unstructured meshes. AIAA Paper 89–0366, 1989.

[3] P–H. Cournède, C. Debiez, A. Dervieux. A positive MUSCL scheme for triangulations. INRIA Report 3465, 1998.

[4] P. Geuzaine. An implicit upwind finire volume method for compressible turbulent flows on unstructured meshes. PhD Thesis, Université de Liège, 1999.

[5] A. Harten, P.D. Lax, B. Van Leer SIAM Review 1983 35 61

[6] R. Hartmann, J. Held, T. Leicht, F. Prill. Discontinuous Galerkin methods for computational aerodynamics–3D adaptive flow simulation with the DLR PADGE code. Aerosp. Sci. Tech., in press (2010), DOI: 10.1016/j.ast.2010.04.002.

[7] O. Hassan, K. Morgan, E. J. Probert, J. Peraire Int. J. Num. Meth. Engg. 1996 549 567

[8] C. Hirsch. Numerical Computation of Internal and External Flows. Volume 2 John Wiley and Sons, Chichester, 1990.

[9] A. Jameson Int. J. CFD 1995 171 218

[10] A. Jameson, T. J. Baker, N. P. Weatherill. Calculation of Inviscid transonic flow over a complete aircraft. AIAA Paper–86–0103, 1986.

[11] A. Jameson, W. Schmidt, E. Turkel. Numerial solution of the Euler equations by finite volume methods using Runge–Kutta time stepping schemes. AIAA Paper 81–1259, 1981.

[12] R. Löhner. Applied CFD Techniques. John Wiley and Sons, Chichester, 2001.

[13] H. Luo, J. D. Baum, R. Löhner AIAA J. 1994 1183 1190

[14] P. R. M. Lyra. Unstructured grid adaptive algorithms for fluid dynamics and heat conduction. PhD Thesis, University of Wales, Swansea, 1994.

[15] D. J. Mavriplis. Revisiting the least–squares procedure for gradient reconstruction on unstructured meshes. AIAA Paper 2003–3986, 2003.

[16] D. J. Mavriplis, V. Venkatakrishnan Int. J. Num. Meth. Fluids 1996 527 544

[17] C. Michalak, C. Ollivier–Gooch J. Comput. Phys. 2009 8693 8711

[18] T. M. Mitchell. Machine Learning. WCB–McGraw–Hill, 1997.

[19] K. Morgan, J. Peraire Rep. Prog. Phys. 1998 569 638

[20] K. Morgan, J. Peraire, J. Peiró, O. Hassan Comp. Meth. Appl. Mech. Engg 1991 335 352

[21] J. Peiró, J. Peraire, K. Morgan. The generation of triangular meshes on surfaces. in C. Creasy and C. Craggs (eds), Applied Surface Modelling, Ellis–Horwood, Chichester, 25–33, 1989.

[22] J. Peraire, J. Peiró, K. Morgan Comp. Mech. 1993 433 451

[23] S. Pirzadeh. Viscous unstructured three–dimensional grids by the advancing–layers method. AIAA–94–0417, 1994.

[24] K. A. Sørensen. A multigrid accelerated procedure for the solution of compressible fluid flows on unstructured hybrid meshes. PhD Thesis, University of Wales, Swansea, 2002.

[25] K. A. Sørensen, O. Hassan, K. Morgan, N. P. Weatherill Comp. Mech. 2003 101 114

[26] P. R. Spalart, S. R. Allmaras. A one–equation turbulent model for aerodynamic flows. AIAA Paper 92–0439, 1992.

[27] T. E. Tezduyar Arch. Comp. Meth. Engg. 2001 83 130

[28] E. F. Toro. Riemann Solvers and Numerical Methods for Fluid Dynamics. A Practical Introduction (2nd edn), Springer, Berlin, 1999.

[29] M. Spruce, W. Speares Shock Waves 1994 25 34

[30] M. Vahdati, K. Morgan, J. Peraire. The computation of viscous compressible flows using an upwind algorithm and unstructured meshes. in S. N. Atluri (ed), Computational Nonlinear Mechanics in Aerospace Engineering, AIAA Progress in Aeronautics and Astronautics Series, AIAA, Washington, 479–505, 1992.

[31] N. P. Weatherill, O. Hassan Int. J. Num. Meth. Engg. 1994 2003 2039

[32] F. M. White. Viscous Fluid Flow (3rd edn). McGraw Hill, Boston, 2006.

Cité par Sources :