Have a personal or library account? Click to login
POD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder Cover

POD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder

Open Access
|Dec 2017

References

  1. 1. M. P. Païdoussis, Fluid-Structure Interactions. Slender Structures and Axial Flow. Volume 1. Academic Press, first ed., 1998.10.1016/S1874-5652(98)80003-3
  2. 2. M. P. Païdoussis, Fluid-Structure Interactions. Slender Structures and Axial Flow. Volume 2. Academic Press, first ed., 2003.
  3. 3. V. Strouhal, Über eine besondere Art der Tonerregung, Annalen der Physik, vol. 241, no. 10, pp. 216-251, 1878.10.1002/andp.18782411005
  4. 4. M. M. Zdravkovich, Flow around Circular Cylinders: Volume 2: Appli- cations, vol. 2. Oxford University Press, 2003. 10.1093/oso/9780198565611.001.0001
  5. 5. M. M. Zdravkovich, Flow around Circular Cylinders: Volume 1: Funda- mentals, vol. 350. Cambridge University Press, 1997.10.1115/1.2819655
  6. 6. R. T. Hartlen and I. G. Currie, Lift-oscillator model of vortex-induced vibration, Journal of the Engineering Mechanics Division, vol. 96, no. 5, pp. 577-591, 1970.10.1061/JMCEA3.0001276
  7. 7. M. Facchinetti, E. de Langre, and F. Biolley, Coupling of structure and wake oscillators in vortex-induced vibrations, Journal of Fluids and Structures, vol. 19, no. 2, pp. 123 - 140, 2004.10.1016/j.jfluidstructs.2003.12.004
  8. 8. G. Stabile, H. G. Matthies, and C. Borri, A novel reduced order model for vortex induced vibrations of long exible cylinders, Submitted to Journal of Ocean Engineering, 2016.
  9. 9. J. S. Hesthaven, G. Rozza, and B. Stamm, Certified Reduced Basis Methods for Parametrized Partial Differential Equations. Springer International Publishing, 2016.10.1007/978-3-319-22470-1
  10. 10. A. Quarteroni, A. Manzoni, and F. Negri, Reduced Basis Methods for Partial Differential Equations. Springer International Publishing, 2016.10.1007/978-3-319-15431-2
  11. 11. B. R. Noack and H. Eckelmann, A low-dimensional Galerkin method for the three-dimensional ow around a circular cylinder, Physics of Fluids, vol. 6, no. 1, pp. 124-143, 1994.10.1063/1.868433
  12. 12. I. Akhtar, A. H. Nayfeh, and C. J. Ribbens, On the stability and extension of reduced-order Galerkin models in incompressible ows, The- oretical and Computational Fluid Dynamics, vol. 23, no. 3, pp. 213-237, 2009.10.1007/s00162-009-0112-y
  13. 13. S. Lorenzi, A. Cammi, L. Luzzi, and G. Rozza, POD-Galerkin method for finite volume approximation of Navier-Stokes and RANS equations, Computer Methods in Applied Mechanics and Engineering, vol. 311, pp. 151 - 179, 2016.10.1016/j.cma.2016.08.006
  14. 14. M. Bergmann, C.-H. Bruneau, and A. Iollo, Enablers for robust POD models, Journal of Computational Physics, vol. 228, no. 2, pp. 516-538, 2009.10.1016/j.jcp.2008.09.024
  15. 15. K. Kunisch and S. Volkwein, Galerkin proper orthogonal decomposition methods for a general equation in uid dynamics, SIAM Journal on Numerical Analysis, vol. 40, no. 2, pp. 492-515, 2002.10.1137/S0036142900382612
  16. 16. J. Burkardt, M. Gunzburger, and H.-C. Lee, POD and CVT-based reduced-order modeling of Navier-Stokes ows, Computer Methods in Applied Mechanics and Engineering, vol. 196, no. 1-3, pp. 337-355, 2006.10.1016/j.cma.2006.04.004
  17. 17. J. Baiges, R. Codina, and S. Idelsohn, Reduced-order modelling strategies for the finite element approximation of the incompressible Navier- Stokes equations, Computational Methods in Applied Sciences, vol. 33, pp. 189-216, 2014.10.1007/978-3-319-06136-8_9
  18. 18. H. K. Versteeg and W. Malalasekera, An Introduction to Computational Fluid Dynamics. The Finite Volume Method. London: Longman Group Ltd., 1995.
  19. 19. F. Moukalled, L. Mangani, and M. Darwish, The Finite Volume Method in Computational Fluid Dynamics: An Advanced Introduction with OpenFOAM and Matlab. Springer Publishing Company, Incorporated, 1st ed., 2015.10.1007/978-3-319-16874-6
  20. 20. H. G.Weller, G. Tabor, H. Jasak, and C. Fureby, A tensorial approach to computational continuum mechanics using object-oriented techniques, Computers in physics, vol. 12, no. 6, pp. 620-631, 1998.10.1063/1.168744
  21. 21. H. Jasak, Error analysis and estimation for the finite volume method with applications to uid ows. PhD thesis, Imperial College, University of London, 1996.
  22. 22. R. Issa, Solution of the implicitly discretised uid ow equations by operator-splitting, Journal of Computational Physics, vol. 62, no. 1, pp. 40-65, 1986.10.1016/0021-9991(86)90099-9
  23. 23. S. Patankar and D. Spalding, A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic ows, International Journal of Heat and Mass Transfer, vol. 15, no. 10, pp. 1787 - 1806, 1972.
  24. 24. A. Caiazzo, T. Iliescu, V. John, and S. Schyschlowa, A numerical investigation of velocity-pressure reduced order models for incompressible ows, Journal of Computational Physics, vol. 259, pp. 598 - 616, 2014.10.1016/j.jcp.2013.12.004
  25. 25. G. Rozza, D. Huynh, and A. Patera, Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations: Application to transport and continuum mechanics, Archives of Computational Methods in Engineering, vol. 15, no. 3, pp. 229-275, 2008.10.1007/s11831-008-9019-9
  26. 26. F. Chinesta, A. Huerta, G. Rozza, and K. Willcox, Model Order Reduction, Encyclopedia of Computational Mechanics, In Press, 2017.
  27. 27. F. Chinesta, P. Ladeveze, and E. Cueto, A Short Review on Model Order Reduction Based on Proper Generalized Decomposition, Archives of Computational Methods in Engineering, vol. 18, no. 4, p. 395, 2011.10.1007/s11831-011-9064-7
  28. 28. A. Dumon, C. Allery, and A. Ammar, Proper general decomposition (PGD) for the resolution of Navier-Stokes equations, Journal of Com- putational Physics, vol. 230, no. 4, pp. 1387-1407, 2011.
  29. 29. L. Sirovich, Turbulence and the Dynamics of Coherent Structures part I: Coherent Structures, Quarterly of Applied Mathematics, vol. 45, no. 3, pp. 561-571, 1987.10.1090/qam/910462
  30. 30. A. Quarteroni and G. Rozza, Numerical solution of parametrized Navier-Stokes equations by reduced basis methods, Numerical Meth- ods for Partial Differential Equations, vol. 23, no. 4, pp. 923-948, 2007. 10.1002/num.20249
  31. 31. G. Rozza, Reduced basis methods for Stokes equations in domains with non-affine parameter dependence, Computing and Visualization in Sci- ence, vol. 12, no. 1, pp. 23-35, 2009.10.1007/s00791-006-0044-7
  32. 32. D. Xiao, F. Fang, A. Buchan, C. Pain, I. Navon, J. Du, and G. Hu, Non linear model reduction for the navier stokes equations using residual deim method, Journal of Computational Physics, vol. 263, pp. 1 - 18, 2014.10.1016/j.jcp.2014.01.011
  33. 33. M. Barrault, Y. Maday, N. C. Nguyen, and A. T. Patera, An 'empirical interpolation' method: application to efficient reduced-basis discretization of partial differential equations, Comptes Rendus Mathematique, vol. 339, no. 9, pp. 667 - 672, 2004.10.1016/j.crma.2004.08.006
  34. 34. K. Carlberg, C. Farhat, J. Cortial, and D. Amsallem, The GNAT method for nonlinear model reduction: Effective implementation and application to computational uid dynamics and turbulent ows, Jour- nal of Computational Physics, vol. 242, pp. 623 - 647, 2013.10.1016/j.jcp.2013.02.028
  35. 35. B. R. Noack, P. Papas, and P. A. Monkewitz, The need for a pressureterm representation in empirical Galerkin models of incompressible shear ows, Journal of Fluid Mechanics, vol. 523, pp. 339-365, 01 2005.10.1017/S0022112004002149
  36. 36. A. E. Deane, I. G. Kevrekidis, G. E. Karniadakis, and S. A. Orszag, Lowdimensional models for complex geometry ows: Application to grooved channels and circular cylinders, Physics of Fluids A: Fluid Dynamics, vol. 3, no. 10, pp. 2337-2354, 1991.
  37. 37. X. Ma and G. Karniadakis, A low-dimensional model for simulating three-dimensional cylinder ow, Journal of Fluid Mechanics, vol. 458, pp. 181-190, 2002.10.1017/S0022112002007991
  38. 38. F. Ballarin, A. Manzoni, A. Quarteroni, and G. Rozza, Supremizer stabilization of POD-Galerkin approximation of parametrized steady incompressible Navier-Stokes equations, International Journal for Nu- merical Methods in Engineering, vol. 102, no. 5, pp. 1136-1161, 2015.
  39. 39. G. Rozza and K. Veroy, On the stability of the reduced basis method for Stokes equations in parametrized domains, Computer Methods in Applied Mechanics and Engineering, vol. 196, no. 7, pp. 1244 - 1260, 2007.
  40. 40. G. Rozza, D. B. P. Huynh, and A. Manzoni, Reduced basis approximation and a posteriori error estimation for Stokes ows in parametrized geometries: Roles of the inf-sup stability constants, Numerische Math- ematik, vol. 125, no. 1, pp. 115-152, 2013.10.1007/s00211-013-0534-8
  41. 41. I. Kalashnikova and M. F. Barone, On the stability and convergence of a Galerkin reduced order model (ROM) of compressible ow with solid wall and far-field boundary treatment, International Journal for Numerical Methods in Engineering, vol. 83, no. 10, pp. 1345-1375, 2010.
  42. 42. S. Sirisup and G. Karniadakis, Stability and accuracy of periodic ow solutions obtained by a POD-penalty method, Physica D: Nonlinear Phenomena, vol. 202, no. 3-4, pp. 218 - 237, 2005.10.1016/j.physd.2005.02.006
  43. 43. W. R. Graham, J. Peraire, and K. Y. Tang, Optimal control of vortex shedding using low-order models. Part I:open-loop model development, International Journal for Numerical Methods in Engineering, vol. 44, no. 7, pp. 945-972, 1999.10.1002/(SICI)1097-0207(19990310)44:7<;945::AID-NME537>3.0.CO;2-F
  44. 44. S. Makridakis, Accuracy measures: theoretical and practical concerns, International Journal of Forecasting, vol. 9, no. 4, pp. 527 - 529, 1993.10.1016/0169-2070(93)90079-3
  45. 45. G. Stabile and G. Rozza, Stabilized Reduced order POD-Galerkin techniques for finite volume approximation of the parametrized Navier- Stokes equations, submitted, 2017.
Language: English
Page range: 210 - 236
Submitted on: Dec 1, 2017
Accepted on: Aug 2, 2017
Published on: Dec 22, 2017
Published by: Italian Society for Applied and Industrial Mathemathics
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2017 Giovanni Stabile, Saddam Hijazi, Andrea Mola, Stefano Lorenzi, Gianluigi Rozza, published by Italian Society for Applied and Industrial Mathemathics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.