Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-27T13:26:50.750Z Has data issue: false hasContentIssue false
  • English
  • Français

Aerodynamic Computations Using a Finite Volume Method with anHLLC Numerical Flux Function

Published online by Cambridge University Press:  16 May 2011

L. Remaki ,
O. Hassan  and
K. Morgan
Get access

Abstract

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 numericalflux function, with acoustic wave improvement. The method is implemented on anunstructured hybrid mesh in three dimensions. A solution of higher order accuracy isobtained by reconstruction, using an iteratively corrected least squares process, and by anew limiting procedure. The numerical performance of the complete approach is demonstratedby considering its application to the simulation of steady turbulent transonic flow overan ONERA M6 wing and to a steady inviscid supersonic flow over a modern military aircraftconfiguration.

Keywords

aerodynamic flowsfinite volume methodHLLC flux functionsolution reconstructionslope limiting
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 3: Computational aerodynamics , 2011 , pp. 189 - 212
Copyright
© EDP Sciences, 2011

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

Références

T. Barth. A 3–D upwind Euler solver for unstructured meshes. AIAA–91–1548–CP, 1991.
T. Barth, D. Jespersen. The design and application of upwind schemes on unstructured meshes. AIAA Paper 89–0366, 1989.
P–H. Cournède, C. Debiez, A. Dervieux. A positive MUSCL scheme for triangulations. INRIA Report 3465, 1998.
P. Geuzaine. An implicit upwind finire volume method for compressible turbulent flows on unstructured meshes. PhD Thesis, Université de Liège, 1999.
Harten, A., Lax, P.D., Van Leer, B.. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Review, 25 (1983), 35–61. CrossRefGoogle Scholar
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.
Hassan, O., Morgan, K., Probert, E. J., Peraire, J.. Unstructured tetrahedral mesh generation for three–dimensional viscous flows. Int. J. Num. Meth. Engg., 39 (1996), 549–567. 3.0.CO;2-O>CrossRefGoogle Scholar
C. Hirsch. Numerical Computation of Internal and External Flows. Volume 2 John Wiley and Sons, Chichester, 1990.
Jameson, A.. Analysis and design of numerical schemes for gas dynamics. 1: artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence. Int. J. CFD, 4 (1995), 171–218. Google Scholar
A. Jameson, T. J. Baker, N. P. Weatherill. Calculation of Inviscid transonic flow over a complete aircraft. AIAA Paper–86–0103, 1986.
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.
R. Löhner. Applied CFD Techniques. John Wiley and Sons, Chichester, 2001.
Luo, H., Baum, J. D., Löhner, R.. Edge–based finite element scheme for the Euler equations. AIAA J., 32 (1994), 1183–1190. CrossRefGoogle Scholar
P. R. M. Lyra. Unstructured grid adaptive algorithms for fluid dynamics and heat conduction. PhD Thesis, University of Wales, Swansea, 1994.
D. J. Mavriplis. Revisiting the least–squares procedure for gradient reconstruction on unstructured meshes. AIAA Paper 2003–3986, 2003.
Mavriplis, D. J., Venkatakrishnan, V.. A 3D agglomeration multigrid solver for the Reynolds–averaged Navier–Stokes equations on unstructured meshes. Int. J. Num. Meth. Fluids, 23 (1996), 527–544. 3.0.CO;2-Z>CrossRefGoogle Scholar
Michalak, C., Ollivier–Gooch, C.. Accuracy preserving limiter for the high–order accurate solution of the Euler equations. J. Comput. Phys., 228 (2009), 8693–8711. CrossRefGoogle Scholar
T. M. Mitchell. Machine Learning. WCB–McGraw–Hill, 1997.
Morgan, K., Peraire, J.. Unstructured grid finite element methods for fluid mechanics. Rep. Prog. Phys., 61 (1998), 569–638. CrossRefGoogle Scholar
Morgan, K., Peraire, J., Peiró, J., Hassan, O.. The computation of three dimensional flows using unstructured grids. Comp. Meth. Appl. Mech. Engg, 87 (1991), 335–352. CrossRefGoogle Scholar
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.
Peraire, J., Peiró, J., Morgan, K.. Finite element multigrid solution of Euler flows past installed aero-engines. Comp. Mech., 11 (1993), 433–451. CrossRefGoogle Scholar
S. Pirzadeh. Viscous unstructured three–dimensional grids by the advancing–layers method. AIAA–94–0417, 1994.
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.
Sørensen, K. A., Hassan, O., Morgan, K., Weatherill, N. P.. A multigrid accelerated hybrid unstructured mesh method for 3D compressible turbulent flow. Comp. Mech., 31 (2003), 101–114. CrossRefGoogle Scholar
P. R. Spalart, S. R. Allmaras. A one–equation turbulent model for aerodynamic flows. AIAA Paper 92–0439, 1992.
Tezduyar, T. E.. Finite element methods for flow problems with moving boundaries and interfaces. Arch. Comp. Meth. Engg., 8 (2001), 83–130. CrossRefGoogle Scholar
E. F. Toro. Riemann Solvers and Numerical Methods for Fluid Dynamics. A Practical Introduction (2nd edn), Springer, Berlin, 1999.
E. F Toro, Spruce, M., Speares, W.. Restoration of the contact surface in the HLL–Riemann Solver. Shock Waves, 4 (1994), 25–34. Google Scholar
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.
Weatherill, N. P., Hassan, O.. Efficient three–dimensional Delaunay triangulation with automatic boundary point creation and imposed boundary constraints. Int. J. Num. Meth. Engg., 37 (1994), 2003–2039. CrossRefGoogle Scholar
F. M. White. Viscous Fluid Flow (3rd edn). McGraw Hill, Boston, 2006.