Immersed boundary methods for the numerical simulation of incompressible aerodynamics and fluid-structure interactions

Nicolas James[1]; Emmanuel Maitre[2]; Iraj Mortazavi[3]

  • [1] LMA Université de Poitiers UMR CNRS 7348 Téléport 2 - BP 30179 Bd Marie et Pierre Curie 86962 Chasseneuil FRANCE
  • [2] LJK Université de Grenoble UMR CNRS 5224 Tour IRMA, BP 53 51, rue des Mathématiques 38041 Grenoble Cedex 9 FRANCE
  • [3] IMB Université de Bordeaux UMR CNRS 5251 MC 2 INRIA Bordeaux Sud-Ouest 351, cours de la libération 33405 Talence FRANCE

Annales mathématiques Blaise Pascal (2013)

  • Volume: 20, Issue: 1, page 139-173
  • ISSN: 1259-1734

Abstract

top
In this work three branches of Immersed Boundary Methods (IBM) are described and validated for incompressible aerodynamics and fluid-structure interactions. These three approaches are: Cut Cell method, Vortex-Penalization method and Forcing method. The first two techniques are validated for external bluff-body flow around a circular obstacle. The last one is used to predict the deformations of an elastic membrane immersed in a fluid. The paper confirms the ability of this family of numerical schemes for accurate and robust simulation of incompressible flows.

How to cite

top

James, Nicolas, Maitre, Emmanuel, and Mortazavi, Iraj. "Immersed boundary methods for the numerical simulation of incompressible aerodynamics and fluid-structure interactions." Annales mathématiques Blaise Pascal 20.1 (2013): 139-173. <http://eudml.org/doc/275509>.

@article{James2013,
abstract = {In this work three branches of Immersed Boundary Methods (IBM) are described and validated for incompressible aerodynamics and fluid-structure interactions. These three approaches are: Cut Cell method, Vortex-Penalization method and Forcing method. The first two techniques are validated for external bluff-body flow around a circular obstacle. The last one is used to predict the deformations of an elastic membrane immersed in a fluid. The paper confirms the ability of this family of numerical schemes for accurate and robust simulation of incompressible flows.},
affiliation = {LMA Université de Poitiers UMR CNRS 7348 Téléport 2 - BP 30179 Bd Marie et Pierre Curie 86962 Chasseneuil FRANCE; LJK Université de Grenoble UMR CNRS 5224 Tour IRMA, BP 53 51, rue des Mathématiques 38041 Grenoble Cedex 9 FRANCE; IMB Université de Bordeaux UMR CNRS 5251 MC 2 INRIA Bordeaux Sud-Ouest 351, cours de la libération 33405 Talence FRANCE},
author = {James, Nicolas, Maitre, Emmanuel, Mortazavi, Iraj},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Immersed boundary method; Momentum forcing method; Vortex penalization method; Cut-cell method; Incompressible viscous flows; Complex geometry; immersed boundary method; momentum forcing method; vortex penalization method; cut-cell method; incompressible viscous flows; complex geometry},
language = {eng},
month = {1},
number = {1},
pages = {139-173},
publisher = {Annales mathématiques Blaise Pascal},
title = {Immersed boundary methods for the numerical simulation of incompressible aerodynamics and fluid-structure interactions},
url = {http://eudml.org/doc/275509},
volume = {20},
year = {2013},
}

TY - JOUR
AU - James, Nicolas
AU - Maitre, Emmanuel
AU - Mortazavi, Iraj
TI - Immersed boundary methods for the numerical simulation of incompressible aerodynamics and fluid-structure interactions
JO - Annales mathématiques Blaise Pascal
DA - 2013/1//
PB - Annales mathématiques Blaise Pascal
VL - 20
IS - 1
SP - 139
EP - 173
AB - In this work three branches of Immersed Boundary Methods (IBM) are described and validated for incompressible aerodynamics and fluid-structure interactions. These three approaches are: Cut Cell method, Vortex-Penalization method and Forcing method. The first two techniques are validated for external bluff-body flow around a circular obstacle. The last one is used to predict the deformations of an elastic membrane immersed in a fluid. The paper confirms the ability of this family of numerical schemes for accurate and robust simulation of incompressible flows.
LA - eng
KW - Immersed boundary method; Momentum forcing method; Vortex penalization method; Cut-cell method; Incompressible viscous flows; Complex geometry; immersed boundary method; momentum forcing method; vortex penalization method; cut-cell method; incompressible viscous flows; complex geometry
UR - http://eudml.org/doc/275509
ER -

References

top
  1. P. Angot, C. -H. Bruneau, P. Fabrie, A penalization method to take into account obstacles in incompressible viscous flows, Numer. Math. 81 (1999), 497-520 Zbl0921.76168MR1675200
  2. J. T. Beale, J. Strain, Locally corrected semi-Lagrangian methods for Stokes flow with moving elastic interfaces, J. Comp. Phys. 227 (2008), 3896-3920 Zbl1146.76044MR2403872
  3. D. Boffi, L. Gastaldi, L. Heltai, Numerical stability of the finite element immersed boundary method, M3AS 17 (2007), 1479-1505 Zbl1186.76661MR2359913
  4. D. Boffia, L. Gastaldi, L. Heltai, Stability results and algorithmic strategies for the finite element approach to the immersed boundary method, preprint available on http://www.ing.unibs.it/~gastaldi/paper.html, Proceeding of the Sixth European Conference on Numerical Mathematics and Advanced Applications (2005), 557-566 Zbl05165537MR2303686
  5. S. Bohnet, R. Ananthakrishnan, A. Mogilner, J.-J. Meister, A. Verkhovsky, Weak force stalls protrusion at the leading edge of the lamellipodium, Biophys. J. 90 (2006), 1810-1820 
  6. F. Bouchon, T. Dubois, N. James, A second-order cut-cell method for the numerical simulation of 2D flows past obstacles, Computers and Fluids 65 (2012), 80-91 MR2966539
  7. D. Bresch, T. Colin, E. Grenier, B. Ribba, O. Saut, Computational modeling of solid tumor growth: the avascular stage, SIAM Journal on Scientific Computing 32 (2010), 2321-2344 Zbl1214.92039MR2678103
  8. D. Bresch, Th. Colin, E. Grenier, B. Ribba, O. Saut, O. Singh, C. Verdier, Quelques méthodes de paramètre d’ordre avec applications à la modélisation de processus cancéreux, ESAIM: Proceedings 18 (2007), 163-180 Zbl05213264MR2404904
  9. Ch. -H. Bruneau, I. Mortazavi, P. Gilliéron, Passive control around the two-dimensional square back Ahmed body using porous devices, J. Fluids Eng. 130 (2008) 
  10. Y.C. Chang, T.Y. Hou, B. Merriman, S. Osher, A Level Set Formulation of Eulerian Interface Capturing Methods for Incompressible Fluid Flows, J. Comp. Phys. 124 (1996), 449-464 Zbl0847.76048MR1383769
  11. Y. Cheny, O. Botella, The LS-STAG method: A new immersed boundary/level-set method for the computation of incompressible viscous flows in complex moving geometries with good conservation properties, J. Comp. phys. 229 (2010), 1043-1076 Zbl1329.76252MR2576238
  12. A.J. Chorin, Vortex sheet approximation of boundary layers, J. Comput. Phys. 27 (1978) Zbl0387.76040
  13. M.-H. Chung, Cartesian cut cell approach for simulating incompressible flows with rigid bodies of arbitrary shape, Computers and Fluids 35 (2006), 607-623 Zbl1160.76369
  14. M. Coquerelle, J. Allard, G. -H. Cottet, M. -P. Cani, A Vortex Method for Bi-phasic Fluids Interacting with Rigid Bodies, Arxiv preprint math, LMC-IMAG (2006) 
  15. M. Coquerelle, G. -H. Cottet, A vortex level set method for the two-way coupling of an incompressible fluid with colliding rigid bodies, J. Comput. Phys. 227 (2008) Zbl1146.76038MR2463201
  16. R. Cortez, C.S. Peskin, J.M. Stockie, D. Varela, Parametric resonance in immersed elastic boundaries, SIAM Journal on Applied Mathematics 65 (2004), 494-520 Zbl1074.74024MR2123067
  17. G. -H. Cottet, F. Gallizio, A. Magni, I. Mortazavi, A vortex immersed boundary method for bluff body flows, ASME Summer Meeting, Montreal FEDSM-ICNMM2010-30787 (2010) 
  18. G. -H. Cottet, P. Koumoutsakos, Vortex Methods: Theory and Practice, (2000) Zbl1140.76002MR1755095
  19. G.-H. Cottet, E. Maitre, A level-set formulation of immersed boundary methods for fluid-structure interaction problems, C. R. Math. 338 (2004), 581-586 Zbl1101.74028MR2057034
  20. G.-H. Cottet, E. Maitre, A level set method for fluid-structure interactions with immersed surfaces, Math. Models Meth. Appl. Sci. 16 (2006), 415-438 Zbl1088.74050MR2238758
  21. G.-H. Cottet, E. Maitre, T. Milcent, Eulerian formulation and level set models for incompressible fluid-structure interaction, ESAIM-Math. Model. Numer. Anal. 42 (2008), 471-492 Zbl1163.76040MR2423795
  22. E. Creusé, A. Giovannini, I. Mortazavi, Vortex simulation of active control strategies for transitional backward-facing step flows, Computers & Fluids 38 (2009) Zbl1242.76226MR2645733
  23. E. A. Fadlun, R. Verzicco, P. Orlandi, J. Mohd-Yusof, Combined immersed-boundary finite difference methods for three-dimensional complex flow simulations, J. Comput. Phys. 161 (2000), 35-60 Zbl0972.76073MR1762073
  24. B.E. Griffith, C.S. Peskin, On the order of accuracy of the immersed boundary method: Higher order convergence rates for sufficiently smooth problems, J. Comp. Phys. 208 (2005), 75-105 Zbl1115.76386MR2144693
  25. F. H. Harlow, J. E. Welch, Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys. Fluids 12 (1965), 2182-2189 Zbl1180.76043
  26. J. Kim, D. Kim, H. Choi, An immersed-boundary finite volume method for simulation of flow in complex geometries, J. Comput. Phys. 171 (2001), 132-150 Zbl1057.76039MR1843643
  27. L. Lee, R.J. Leveque, An immersed interface method for incompresible Navier-Stokes equations, SIAM J. Sci. Comp. 25 (2003), 832-856 Zbl1163.65322MR2046114
  28. R. J. LeVeque, Z. Li, The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources, SIAM J. Numer. Anal. 31 (1994), 1019-1044 Zbl0811.65083MR1286215
  29. R. J. LeVeque, Z. Li, Immersed interface methods for Stokes flow with elastic boundaries or surface tension, SIAM J. Sci. Comput. 18 (1997), 709-735 Zbl0879.76061MR1443639
  30. N. Matsunaga, Y. Yamamoto, Superconvergence of the shortley-weller approximation for dirichlet problems, J. Comp. Appl. Math. 116 (2000), 263-273 Zbl0952.65082MR1750921
  31. T. Milcent, Formulation eulerienne du couplage fluide structure, analyse mathématique et applications en biomécanique, (2008), Thèse de l’Université de Grenoble 
  32. R. Mittal, H. Dong, M. Bozkurttas, F. M. Najjar, A. Vargas, A. V. Loebbecke, A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries, J. Comput. Phys. 227 (2008), 4825-4852 Zbl05276051MR2414837
  33. R. Mittal, G. Iaccarino, Immersed Boundary Methods, Annual Review of Fluid Mechanics 37 (2005), 239-261 Zbl1117.76049MR2115343
  34. J. Mohd-Yusof, Combined immersed-boundary/B-Spline methods for simulations of flow in complex geometries, (1997), 317-327, NASA Ames Research Center/Stanford University 
  35. I. Mortazavi, A. Giovannini, The simulation of vortex dynamics downstream of a plate separator using a vortex-finite element method, Int. J. Fluid Dynamics 5 (2001) 
  36. F. Muldoon, S. Acharya, A divergence-free interpolation scheme for the immersed boundary method, Int. J. Numer. Method Fluid 56 (2008), 1845-1884 Zbl1262.76077MR2397813
  37. F. Noca, D. Shiels, D. Jeon, A comparison of methods for evaluating time-dependent fluid dynamic forces on bodies, using only velocity fields and their derivatives, Journal of Fluids and Structures 13 (1999) 
  38. D. Olz, C. Schmeiser, V. Small, Modelling of the Actin-cytoskeleton in symmetric lamellipodial fragments, Cell Adhesion and Migration 2 (2008), 117-126 
  39. S. Osher, R. P. Fedkiw, Level set methods and Dynamic Implicit Surfaces, (2003), Springer Zbl1026.76001MR1939127
  40. S. Osher, J. A. Sethian, Fronts Propagating with Curvature Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations, J. Comput. Phys. 79 (1988), 12-49 Zbl0659.65132MR965860
  41. C. S. Peskin, The fluid dynamics of heart valves: experimental, theoretical, and computational methods, Ann. Rev. Fluid Mech. 14 (1982), 235-259 Zbl0488.76129MR642539
  42. C. S. Peskin, The immersed boundary method, Acta Numerica 11 (2002), 1-39 Zbl1123.74309MR2009378
  43. C.S. Peskin, Numerical Analysis of Blood Flow in the Heart, J. Comp. Phys. 25 (1977), 220-252 Zbl0403.76100MR490027
  44. S. Peskin, B.F. Printz, Improved volume conservation in the computation of flows with immersed boundaries, J. Comput. Phys. 105 (1993), 33-46 Zbl0762.92011MR1210858
  45. P. Ploumhans, G. S. Winckelmans, Vortex methods for high-resolution simulations of viscous flow past bluff bodies of general geometry, Journal of Computational Physics 165 (2000) Zbl1006.76068MR1807293
  46. E. M. Saiki, S. Biringen, Numerical simulation of a cylinder in uniform flow: application of a virtual boundary method, J. Comput. Phys. 123 (1996), 450-465 Zbl0848.76052
  47. J. Stockie, Analysis of Stiffness in the immersed boundary method and implications for time-stepping schemes, J. Comp. Phys. 154 (1999), 41-64 Zbl0953.76070
  48. P. G. Tucker, Z. Pan, A cartesian cut-cell method for incompressible viscous flow, Appl. Math. Model. 24 (2000), 591-606 Zbl1056.76059
  49. M. De Tullio, A. Cristallo, E. Balaras, G. Pascazio, P. De Palma, G. Iaccarino, M. Napolitano, R. Verzicco, Recent advances in the immersed boundary method, ECCOMAS CFD (2006), WesselingP.P. 
  50. T. Ye, R. Mittal, H. S. Udaykumar, W. Shyy., Numerical Simulation of two-dimensional flows over a circular cylinder using the immersed boundary method, J. Comp. Phys. 156 (1999), 209-240 Zbl0957.76043
  51. N. Zhang, Z. C. Zheng, An Improved Direct-Forcing Immersed Boundary Method for Finite Difference Applications, J. Comput. Phys. 221 (2007), 250-268 Zbl1108.76051MR2290571

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.