Aerodynamic Computations Using a Finite Volume Method with an HLLC Numerical Flux Function

L. Remaki; O. Hassan; K. Morgan

Mathematical Modelling of Natural Phenomena (2011)

  • Volume: 6, Issue: 3, page 189-212
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Remaki, L., Hassan, O., and Morgan, K.. "Aerodynamic Computations Using a Finite Volume Method with an HLLC Numerical Flux Function." Mathematical Modelling of Natural Phenomena 6.3 (2011): 189-212. <http://eudml.org/doc/222299>.

@article{Remaki2011,
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 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.},
author = {Remaki, L., Hassan, O., Morgan, K.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {aerodynamic flows; finite volume method; HLLC flux function; solution reconstruction; slope limiting},
language = {eng},
month = {5},
number = {3},
pages = {189-212},
publisher = {EDP Sciences},
title = {Aerodynamic Computations Using a Finite Volume Method with an HLLC Numerical Flux Function},
url = {http://eudml.org/doc/222299},
volume = {6},
year = {2011},
}

TY - JOUR
AU - Remaki, L.
AU - Hassan, O.
AU - Morgan, K.
TI - Aerodynamic Computations Using a Finite Volume Method with an HLLC Numerical Flux Function
JO - Mathematical Modelling of Natural Phenomena
DA - 2011/5//
PB - EDP Sciences
VL - 6
IS - 3
SP - 189
EP - 212
AB - 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.
LA - eng
KW - aerodynamic flows; finite volume method; HLLC flux function; solution reconstruction; slope limiting
UR - http://eudml.org/doc/222299
ER -

References

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  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. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Review, 25 (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: .  URI10.1016/j.ast.2010.04.002
  7. O. Hassan, K. Morgan, E. J. Probert, J. Peraire. Unstructured tetrahedral mesh generation for three–dimensional viscous flows. Int. J. Num. Meth. Engg., 39 (1996), 549–567.  
  8. C. Hirsch. Numerical Computation of Internal and External Flows. Volume 2 John Wiley and Sons, Chichester, 1990.  
  9. A. Jameson. 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.  
  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. Edge–based finite element scheme for the Euler equations. AIAA J., 32 (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. A 3D agglomeration multigrid solver for the Reynolds–averaged Navier–Stokes equations on unstructured meshes. Int. J. Num. Meth. Fluids, 23 (1996), 527–544.  
  17. C. Michalak, C. Ollivier–Gooch. Accuracy preserving limiter for the high–order accurate solution of the Euler equations. J. Comput. Phys., 228 (2009), 8693–8711.  
  18. T. M. Mitchell. Machine Learning. WCB–McGraw–Hill, 1997.  
  19. K. Morgan, J. Peraire. Unstructured grid finite element methods for fluid mechanics. Rep. Prog. Phys., 61 (1998), 569–638.  
  20. K. Morgan, J. Peraire, J. Peiró, O. Hassan. The computation of three dimensional flows using unstructured grids. Comp. Meth. Appl. Mech. Engg, 87 (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. Finite element multigrid solution of Euler flows past installed aero-engines. Comp. Mech., 11 (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. A multigrid accelerated hybrid unstructured mesh method for 3D compressible turbulent flow. Comp. Mech., 31 (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. Finite element methods for flow problems with moving boundaries and interfaces. Arch. Comp. Meth. Engg., 8 (2001), 83–130.  
  28. E. F. Toro. Riemann Solvers and Numerical Methods for Fluid Dynamics. A Practical Introduction (2nd edn), Springer, Berlin, 1999.  
  29. E. F Toro, M. Spruce, W. Speares. Restoration of the contact surface in the HLL–Riemann Solver. Shock Waves, 4 (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. Efficient three–dimensional Delaunay triangulation with automatic boundary point creation and imposed boundary constraints. Int. J. Num. Meth. Engg., 37 (1994), 2003–2039.  
  32. F. M. White. Viscous Fluid Flow (3rd edn). McGraw Hill, Boston, 2006.  

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