Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
권호 표지
DOI QR코드

DOI QR Code

THE ISOGEOMETRIC VARIATIONAL MULTISCALE METHOD FOR LAMINAR INCOMPRESSIBLE FLOW

  • Received : 2012.01.03
  • Accepted : 2012.03.16
  • Published : 2012.03.25
Download PDF
⟨ Previous Next ⟩

Abstract

We present an application of the variational multiscale methodology to the computation of concentric annular pipe flow. Isogeometric analysis is utilized for higher order approximation of the solution using Non-Uniform Rational B-Splines (NURBS) functions. The ability of NURBS to exactly represent curved geometries makes NURBS-based isogeometric analysis attractive for the application to the flow through the curved channel.

Keywords

References

  1. I.Akkerman, Y. Bazilevs, V.M. Calo, T.R.J. Hughes and S. Hulshof, The role of continuity in residual-based variational multiscale modeling of turbulence, Computational Mechanics., 41 (2008), 371-78.
  2. Y. Bazilevs, L. Beirao de Veiga, J.A. Cottrell, T.J.R. Hughes, G. Sangali, Isogeometric analysis: approximation, stability and error estimates for h-refine meshes, Mathematical Models and Methods in applied Science, 16 (2006), 1-60. https://doi.org/10.1142/S0218202506001030
  3. Y. Bazilevs, V.M. Calo, J.A. Cottrell, T.J.R Hughes, A. Reali and G. Scovazzi, Variational multiscale residualbased turbulence modeling for large eddy simulation of incompressible flows, Comput. Methods Appl. Mech. Eng., 197 (2007), 173-201. https://doi.org/10.1016/j.cma.2007.07.016
  4. A.N. Brooks and T.J.R. Hughes, Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comput Methods Appl. Mech. Eng., 32 1989, 199-259.
  5. V.M. Calo, Residual-based Multiscale Turbulence Modeling:Finite Volume Simulation of Bypass Transition, PhD thesis, Department of Civil and Environmental Engineering, Standford University, 2004.
  6. J. Chung and G.A. Hulbert, A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized alpha - method, J. Appl. Mech., 60 (1993), 371-75. https://doi.org/10.1115/1.2900803
  7. R. Codina, J. Principe, O. Guasch and S. Badia, Time dependent subscales in the stabilized finite element approximation of incompressible flow problems, Comput. Methods Appl. Mech. Eng., 196 (2007), 2413-30. https://doi.org/10.1016/j.cma.2007.01.002
  8. J.A. Cottrell, T.J.R. Hughes and Y.Bazilevs, Isogeometric Analysis. Towards integration of CAD and FEA, Wiley, 2009.
  9. J. A. Cottrell, T.J.R. Hughes and A. Reali, Studies of Refinement and Continuity in Isogeometric Structural Analysis, Comput. Methods Appl. Mech. Eng., 196 (2007) , 4160-4183. https://doi.org/10.1016/j.cma.2007.04.007
  10. Y. Ghaffari Motlagh, H.T. Ahn, Laminar and turbulent channel flow simulation using residual based variational multi-scale method, JMST, 26 (2012) ,447-454.
  11. J. Holmen, T.J.R. Hughes, A.A. Oberai and G.N. Wells, Sensitivity of the scale partition for variational multiscale LES of channel flow, Phys. Fluids, 16 (2004),824-827. https://doi.org/10.1063/1.1644573
  12. T.J.R. Hughes, Multiscale phenomena: Green functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and origins of stabilized methods, Comput. Methods Appl. Mech. Eng., 127 (1995), 387-401. https://doi.org/10.1016/0045-7825(95)00844-9
  13. T.J.R. Hughes, V.M. Calo and G. Scovazzi, Variational and multiscale methods in turbulence in: W.Gutkowski,T.A. Kowalewski (Eds.), Proceedings of the XXI International Congress of Theoretical and Applied Mechanics (IUTAM), Kluwer,2004.
  14. T.J.R. Hughes, J.A. Cottrell and Y. Bazilevs, Isogeometric analysis: CAD,finite elements, NURBS, exact geometry, and mesh refinement, Comput. Methods. Appl. Mech. Eng., 194 (2005), 4135-4195. https://doi.org/10.1016/j.cma.2004.10.008
  15. T.J.R Hughes, L.P. Franca and G. Hulbert, A new finite element formulation for computational fluid dynamics: VIII. The Galerkin least squares method for advective-diffusive equations, Comput. Methods Appl. Mech. Eng., 73 (1989), 173-189. https://doi.org/10.1016/0045-7825(89)90111-4
  16. T.J.R. Hughes and M. Mallet, A few finite element formulation for fluid dynamics: III. The generalized streamline operator for multidimensional advective-diffusive systems, Comput Methods Appl Mech Eng 85 (1986), 305-328.
  17. T.J.R. Hughes and G. Sangalli, Variational multiscale analysis: The fine-scale Green's function, projection, optimization, localization, and stabilized methods, SIAM Journal on Numerical Analysis, 45 (2007), 539-557. https://doi.org/10.1137/050645646
  18. T.J.R. Hughes, G. Scovazzi and L.P. Franca, Multiscale and stabilized methods, in: E. Stein,R. de Borst,T.J.R. Hughes (Eds.),Encyclopedia of Computational Mechanics, Computational Fluid Dynamics, 3, Wiley, 2004.
  19. K.E. Jansen, C.H. Whiting and G.M. Hulbert, A generalized alpha-method for integrating the filtered Navier- Stokes equations with a stabilized finite element method, Comput. Methods Appl. Mech. Eng., 190 (1999), 305-319.
  20. L. Piegl, W. Tiller, The NURBS book,Monographs in visual communication,second ed., Springer-Verlag, New York,1997.
  21. F.M. White, Fliud Mechanics ,third ed., Mc Graw-Hill, New York,1994.