Engineering with Computers

, 24:267 | Cite as

Adaptive boundary layer meshing for viscous flow simulations

  • Onkar Sahni
  • Kenneth E. Jansen
  • Mark S. Shephard
  • Charles A. Taylor
  • Mark W. Beall
Regular Article

Abstract

A procedure for anisotropic mesh adaptation accounting for mixed element types and boundary layer meshes is presented. The method allows to automatically construct meshes on domains of interest to accurately and efficiently compute key flow quantities, especially near wall quantities like wall shear stress. The new adaptive approach uses local mesh modification procedures in a manner that maintains layered and graded elements near the walls, which are popularly known as boundary layer or semi-structured meshes, with highly anisotropic elements of mixed topologies. The technique developed is well suited for viscous flow applications where exact knowledge of the mesh resolution over the computational domain required to accurately resolve flow features of interest is unknown a priori. We apply the method to two types of problem cases; the first type, which lies in the field of hemodynamics, involves pulsatile flow in blood vessels including a porcine aorta case with a stenosis bypassed by a graft whereas the other involves high-speed flow through a double throat nozzle encountered in the field of aerodynamics.

Keywords

Boundary layer meshes Computational fluid dynamics Mesh adaptation Mixed/hybrid meshes Viscous flow simulations 

References

  1. 1.
    Sahni O, Müller J, Jansen KE, Shephard MS, Taylor CA (2006) Efficient anisotropic adaptive discretization of the cardiovascular system. Comp Meth Appl Mech Eng 195:5634–5655CrossRefMATHGoogle Scholar
  2. 2.
    Pirzadeh S (1994) Unstructured viscous grid generation by the advancing-layers method. AIAA J 32:1735–1737CrossRefGoogle Scholar
  3. 3.
    Connell SD, Braaten ME (1995) Semi-structured mesh generation for three-dimensional Navier–Stokes calculations. AIAA J 33:1017–1024CrossRefMATHGoogle Scholar
  4. 4.
    Garimella RV, Shephard MS (2000) Boundary layer mesh generation for viscous flow simulations. Int J Numer Meth Eng 49:193–218CrossRefMATHGoogle Scholar
  5. 5.
    Ito Y, Nakahashi K (2002) Unstructured mesh generation for viscous flow computations. In: Proceedings of 11th Internatinal Meshing Roundtable, IthacaGoogle Scholar
  6. 6.
    Jansen KE, Shephard MS, Beall MW (2001) On anisotropic mesh generation and quality control in complex flow problems. In: Proceedings of 10th Internatinal Meshing Roundtable, Newport BeachGoogle Scholar
  7. 7.
    Khawaja A, Kallinderis Y (2000) Hybrid grid generation for turbomachinery and aerospace applications. Int J Numer Meth Eng 49:145–166CrossRefMATHGoogle Scholar
  8. 8.
    Löhner R, Cebral J (2000) Generation of non-isotropic unstructured grids via directional enrichment. Int J Numer Meth Eng 49:219–232CrossRefMATHGoogle Scholar
  9. 9.
    Peraire J, Vahdati M, Morgan K, Zienkiewicz OC (1987) Adaptive remeshing for compressible flow computations. J Comput Phys 72:449–466CrossRefMATHGoogle Scholar
  10. 10.
    Buscaglia GC, Dari EA (1997) Anisotropic mesh optimization and its application in adaptivity. Int J Numer Meth Eng 40:4119–4136CrossRefMATHGoogle Scholar
  11. 11.
    Castro-Diáz MJ, Hecht F, Mohammadi B, Pironneau O (1997) Anisotropic unstructured mesh adaption for flow simulations. Int J Numer Meth Fluids 25:475–491CrossRefMATHGoogle Scholar
  12. 12.
    Frey PJ, Alauzet F (2005) Anisotropic mesh adaptation for CFD computations. Comp Meth Appl Mech Eng 194:5068–5082CrossRefMathSciNetMATHGoogle Scholar
  13. 13.
    Li X, Shephard MS, Beall MW (2005) 3D anisotropic mesh adaptation by mesh modifications. Comp Meth Appl Mech Eng 194:4915–4950CrossRefMathSciNetMATHGoogle Scholar
  14. 14.
    Li X, Shephard MS, Beall MW (2003) Accounting for curved domains in mesh adaptation. Int J Numer Meth Eng 58:247–276CrossRefMATHGoogle Scholar
  15. 15.
    Müller J, Sahni O, Li X, Jansen KE, Shephard MS, Taylor CA (2005) Anisotropic adaptive finite element method for modelling blood flow. Comp Meth Biomech Biomed Eng 8:295–305CrossRefGoogle Scholar
  16. 16.
    Pain CC, Umpleby AP, de Oliveira CRE, Goddard AJH (2001) Tetrahedral mesh optimisation and adaptivity for steady-state and transient finite element calculations. Comp Meth Appl Mech Eng 190:3771–3796CrossRefMATHGoogle Scholar
  17. 17.
    Remacle JF, Li X, Shephard MS, Flaherty JE (2005) Anisotropic adaptive simulation of transient flows using discontinuous Galerkin methods. Int J Numer Meth Eng 62:899–923CrossRefMathSciNetMATHGoogle Scholar
  18. 18.
    Khawaja A, Minyard T, Kallinderis Y (2000) Adaptive hybrid grid methods. Comp Meth Appl Mech Eng 189:1231–1245CrossRefMATHGoogle Scholar
  19. 19.
    Kallinderis Y, Kavouklis C (2005) A dynamic adaptation scheme for general 3-D hybrid meshes. Comp Meth Appl Mech Eng 194:5019–5050CrossRefMATHGoogle Scholar
  20. 20.
    Garimella RV (1999) Anisotropic tetrahedral mesh generation. PhD Thesis, Rensselaer Polytechnic Institute Google Scholar
  21. 21.
    Freitag LA, Ollivier-Gooch C (1997) Tetrahedral mesh improvement using swapping and smoothing. Int J Numer Method Eng 40:3979–4002CrossRefMathSciNetMATHGoogle Scholar
  22. 22.
    Ku JP, Draney MT, Arko FR, Lee WA, Chan FP, Pelc NJ, Zarins CK, Taylor CA (2002) In vivo validation of numerical prediction of blood flow in arterial bypass grafts. Ann Biomed Eng 30:743–752CrossRefGoogle Scholar
  23. 23.
    Taylor CA, Hughes TJR, Zarins CK (1998) Finite element modeling of blood flow in arteries. Comp Meth Appl Mech Eng 158:155–196CrossRefMathSciNetMATHGoogle Scholar
  24. 24.
    Taylor CA, Draney M, Ku J, Parker D, Steel B, Wang K, Zarins C(1999) Predictive medicine: computational techniques in therapeutic decision-making. Comp Aided Surg 4(5):231–247CrossRefGoogle Scholar
  25. 25.
    Stuhne GR, Steinman DA (2004) Finite-element modeling of the hemodynamics of stented aneurysms. Trans ASME J Biomech Eng 126(3):382–387CrossRefGoogle Scholar
  26. 26.
    Bristeau MO, Glowinski R, Periaux J, Viviand H (1987) Presentation of problems and discussion of results. In: Bristeau MO, Glowinski R, Periaux J, Viviand H (eds) Numerical simulation of compressible Navier–Stokes flows, notes on numerical fluid mechanics, vol 18, Vieweg, pp 1–40Google Scholar
  27. 27.
    Figueroa CA, Vignon-Clementel IE, Jansen KE, Hughes TJR, Taylor CA (2006) A coupled momentum method for modeling blood flow in three-dimensional deformable arteries. Comp Meth Appl Mech Eng 195:5685–5706CrossRefMathSciNetMATHGoogle Scholar
  28. 28.
    Brooks AN, Hughes TJR (1982) Streamline upwind/Petrov–Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. Comp Meth Appl Mech Eng 32:199–259CrossRefMathSciNetMATHGoogle Scholar
  29. 29.
    Whiting CH, Jansen KE (2001) A stabilized finite element method for the incompressible Navier–Stokes equations using a hierarchical basis. Int J Numer Meth Fluids 35:93–116CrossRefMATHGoogle Scholar
  30. 30.
    Jansen KE, Whiting CH, Hulbert GM (1999) A generalized-α method for integrating the filtered Navier–Stokes equations with a stabilized finite element method. Comp Meth Appl Mech Eng 190: 305–319CrossRefMathSciNetGoogle Scholar
  31. 31.
  32. 32.
    Womersley J (1955) Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. J Physiol (Lond) 127:553–563Google Scholar
  33. 33.
    Vignon-Clementel IE, Figueroa CA, Jansen KE, Taylor CA (2006) Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries. Comp Meth Appl Mech Eng 195:3776–3796CrossRefMathSciNetMATHGoogle Scholar
  34. 34.
    Hughes TJR, Franca LP, Mallet M (1986) A new finite element formulation for computational fluid dynamics: I. Symmetric forms of the compressible Euler and Navier–Stokes equations and the second law of thermodynamics. Comp Meth Appl Mech Eng 54:223–234CrossRefMathSciNetMATHGoogle Scholar
  35. 35.
    Whiting CH, Jansen KE, Dey S (2003) Hierarchical basis in stabilized finite element methods for compressible flows. Comp Meth Appl Mech Eng 192:5167–5185CrossRefMATHGoogle Scholar
  36. 36.
    Hughes TJR, Franca LP, Mallet M (1986) A new finite element formulation for computational fluid dynamics: IV. A discontinuity-capturing operator for multidimensional advective-diffusive systems. Comp Meth Appl Mech Eng 58:329–336CrossRefMathSciNetMATHGoogle Scholar
  37. 37.
    Saad Y, Schultz M (1986) GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput 7:856–869CrossRefMathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2008

Authors and Affiliations

  • Onkar Sahni
    • 1
  • Kenneth E. Jansen
    • 1
  • Mark S. Shephard
    • 1
  • Charles A. Taylor
    • 2
  • Mark W. Beall
    • 3
  1. 1.Scientific Computation Research CenterRensselaer Polytechnic InstituteTroyUSA
  2. 2.E350 Clark CenterStanford UniversityStanfordUSA
  3. 3.Simmetrix IncClifton ParkUSA

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