Skip to main content
SpringerLink
Log in

A Lagrangian–Lagrangian Framework for the Simulation of Rigid and Deformable Bodies in Fluid

  • Chapter
  • First Online:
Multibody Dynamics

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 35))

Abstract

We present a Lagrangian–Lagrangian approach for the simulation of fully resolved Fluid Solid/Structure Interaction (FSI) problems. In the proposed approach, the method of Smoothed Particle Hydrodynamics (SPH) is used to simulate the fluid dynamics in a Lagrangian framework. The solid phase is a general multibody dynamics system composed of a collection of interacting rigid and deformable objects. While the motion of arbitrarily shaped rigid objects is approached in a classical 3D rigid body dynamics framework, the Absolute Nodal Coordinate Formulation (ANCF) is used to model the deformable components, thus enabling the investigation of compliant elements that experience large deformations with entangling and self-contact. The dynamics of the two phases, fluid and solid, are coupled with the help of Lagrangian markers, referred to as Boundary Condition Enforcing (BCE) markers which are used to impose no-slip and impenetrability conditions. Such BCE markers are associated both with the solid suspended particles and with any confining boundary walls and are distributed in a narrow layer on and below the surface of solid objects. The ensuing fluid–solid interaction forces are mapped into generalized forces on the rigid and flexible bodies and subsequently used to update the dynamics of the solid objects according to rigid body motion or ANCF method. The robustness and performance of the simulation algorithm is demonstrated through several numerical simulation studies.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Amini Y, Emdad H, Farid M (2011) A new model to solve fluid-hypo-elastic solid interaction using the smoothed particle hydrodynamics (SPH) method. Eur J Mech B Fluids 30(2):184–194

    Article  MATH  Google Scholar 

  2. Andrews M, O’rourke P (1996) The multiphase particle-in-cell (MP-PIC) method for dense particulate flows. Int J Multiph Flow 22(2):379–402

    Google Scholar 

  3. Anitescu M, Hart GD (2004) A constraint-stabilized time-stepping approach for rigid multibody dynamics with joints, contact and friction. Int J Numer Meth Eng 60(14):2335–2371

    Google Scholar 

  4. Antoci C, Gallati M, Sibilla S (2007) Numerical simulation of fluid-structure interaction by SPH. Comput Struct 85(11):879–890

    Google Scholar 

  5. Atkinson K (1989) An introduction to numerical analysis. Wiley, USA

    MATH  Google Scholar 

  6. Benz W (1986) Smoothed particle hydrodynamics: a review. In: Proceedings of the NATO advanced research workshop on the numerical modelling of nonlinear stellar pulsations problems and prospects, Les Arcs, France, 20–24 Mar. Kluwer Academic Publishers, Berlin

    Google Scholar 

  7. Brenner H (1961) The slow motion of a sphere through a viscous fluid towards a plane surface. Chem Eng Sci 16(3):242–251

    Article  Google Scholar 

  8. Chrono::Fluid (2014) An open source engine for fluid. Solid interaction. http://armanpazouki.github.io/chrono-fluid

  9. Colagrossi A, Landrini M (2003) Numerical simulation of interfacial flows by smoothed particle hydrodynamics. J Comput Phys 191(2):448–475

    Article  MATH  Google Scholar 

  10. Davis RH, Serayssol JM, Hinch E (1986) Elastohydrodynamic collision of two spheres. J Fluid Mech 163:479–497

    Article  Google Scholar 

  11. Dilts G (1999) Moving-least-squares-particle hydrodynamics-I. Consistency and stability. Int J Numer Methods Eng 44(8):1115–1155

    Article  MATH  MathSciNet  Google Scholar 

  12. Ding EJ, Aidun CK (2003) Extension of the lattice-Boltzmann method for direct simulation of suspended particles near contact. J Stat Phys 112(3–4):685–708

    Article  MATH  Google Scholar 

  13. Durlofsky L, Brady JF, Bossis G (1987) Dynamic simulation of hydrodynamically interacting particles. J Fluid Mech 180(1):21–49

    Article  MATH  Google Scholar 

  14. Fan LS, Zhu C (2005) Principles of gas-solid flows. Cambridge University Press, Cambridge

    Google Scholar 

  15. Gerstmayr J, Shabana A (2006) Analysis of thin beams and cables using the absolute nodal co-ordinate formulation. Nonlinear Dyn 45(1):109–130

    Article  MATH  Google Scholar 

  16. Gidaspow D (1994) Multiphase flow and fluidization: continuum and kinetic theory descriptions. Academic Press, Boston

    MATH  Google Scholar 

  17. Glowinski R, Pan T, Hesla T, Joseph D (1999) A distributed Lagrange multiplier/fictitious domain method for particulate flows. Int J Multiph Flow 25(5):755–794

    Article  MATH  Google Scholar 

  18. Haug E (1989) Computer aided kinematics and dynamics of mechanical systems. Allyn and Bacon, Boston

    Google Scholar 

  19. Hoberock J, Bell N Thrust: C++ template library for CUDA. http://thrust.github.com/

  20. Hocking L (1973) The effect of slip on the motion of a sphere close to a wall and of two adjacent spheres. J Eng Math 7(3):207–221

    Article  MATH  Google Scholar 

  21. Hu H, Patankar N, Zhu M (2001) Direct numerical simulations of fluid-solid systems using the arbitrary Lagrangian–Eulerian technique. J Comput Phys 169(2):427–462

    Article  MATH  MathSciNet  Google Scholar 

  22. Hu W, Tian Q, Hu H (2013) Dynamic simulation of liquid-filled flexible multibody systems via absolute nodal coordinate formulation and SPH method. Nonlinear Dyn, pp 1–19

    Google Scholar 

  23. Kruggel-Emden H, Simsek E, Rickelt S, Wirtz S, Scherer V (2007) Review and extension of normal force models for the discrete element method. Powder Technol 171(3):157–173

    Article  Google Scholar 

  24. Kruggel-Emden H, Wirtz S, Scherer V (2008) A study on tangential force laws applicable to the discrete element method (DEM) for materials with viscoelastic or plastic behavior. Chem Eng Sci 63(6):1523–1541

    Article  Google Scholar 

  25. Ladd AJ (1994) Numerical simulations of particulate suspensions via a discretized Boltzmann equation. J Fluid Mech 271(1):285–339

    Article  MATH  MathSciNet  Google Scholar 

  26. Ladd AJ (1997) Sedimentation of homogeneous suspensions of non-brownian spheres. Phys Fluids 9:491

    Article  Google Scholar 

  27. Ladd A, Verberg R (2001) Lattice-Boltzmann simulations of particle-fluid suspensions. J Stat Phys 104(5–6):1191–1251

    Article  MATH  MathSciNet  Google Scholar 

  28. Lee CJK, Noguchi H, Koshizuka S (2007) Fluid-shell structure interaction analysis by coupled particle and finite element method. Comput Struct 85(11):688–697

    Article  Google Scholar 

  29. Liu M, Liu G (2010) Smoothed particle hydrodynamics (SPH): an overview and recent developments. Arch Computat Methods Eng 17(1):25–76

    Article  Google Scholar 

  30. McLaughlin J (1994) Numerical computation of particles-turbulence interaction. Int J Multiph Flow 20:211–232

    Article  MATH  Google Scholar 

  31. Monaghan JJ (1988) An introduction to SPH. Comput Phys Comm 48(1):89–96

    Article  MATH  Google Scholar 

  32. Monaghan J (1989) On the problem of penetration in particle methods. J Comput Phys 82(1):1–15

    Article  MATH  Google Scholar 

  33. Monaghan JJ (1992) Smoothed particle hydrodynamics. Ann Rev Astron Astrophys 30:543–574

    Article  Google Scholar 

  34. Monaghan J (2005) Smoothed particle hydrodynamics. Rep Prog Phys 68(1):1703–1759

    Article  MathSciNet  Google Scholar 

  35. Morris J, Fox P, Zhu Y (1997) Modeling low Reynolds number incompressible flows using SPH. J Computat Phys 136(1):214–226

    Article  MATH  Google Scholar 

  36. Negrut D, Tasora A, Mazhar H, Heyn T, Hahn P (2012) Leveraging parallel computing in multibody dynamics. Multibody Sys Dyn 27(1):95–117

    Article  MATH  Google Scholar 

  37. NVIDIA: CUDA developer zone (2014). https://developer.nvidia.com/cuda-downloads

  38. Pazouki A, Negrut D (2012) Direct simulation of lateral migration of buoyant particles in channel flow using GPU computing. In: Proceedings of the 32nd computers and information in engineering conference, CIE32, 12–15 Aug 2012. American Society of Mechanical Engineers, Chicago, IL, USA

    Google Scholar 

  39. Pazouki A, Negrut D A numerical study of the effect of particle properties on the radial distribution of suspensions in pipe flow. Submitted to International Journal of Multiphase Flow

    Google Scholar 

  40. Sader J (1998) Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope. J Appl Phys 84(1):64–76

    Article  Google Scholar 

  41. SBEL: Vimeo page (2014). https://vimeo.com/uwsbel

  42. Schörgenhumer M, Gruber PG, Gerstmayr J (2013) Interaction of flexible multibody systems with fluids analyzed by means of smoothed particle hydrodynamics. Multibody Sys Dyn, pp 1–24

    Google Scholar 

  43. Schwab A, Meijaard J (2005) Comparison of three-dimensional flexible beam elements for dynamic analysis: finite element method and absolute nodal coordinate formulation. In: Proceedings of the ASME 2005 IDETC/CIE, Orlando, Florida

    Google Scholar 

  44. Shabana A (2005) Dynamics of multibody systems. Cambridge University Press, New York

    Google Scholar 

  45. Shabana A (1997) Flexible multibody dynamics: review of past and recent developments. Multibody Sys Dyn 1:339–348

    Article  MATH  MathSciNet  Google Scholar 

  46. Zhang D, Prosperetti A (1994) Averaged equations for inviscid disperse two-phase flow. J Fluid Mech 267:185–220

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

Financial support was provided in part by the National Science Foundation (grant NSF CMMI-084044). Support for the second and third authors was provided in part by Army Research Office awards W911NF-11-0327 and W911NF-12-1-0395. NVIDIA is acknowledged for providing the GPU hardware used in generating the simulation results reported herein.

Author information

Authors and Affiliations

  1. University of Wisconsin-Madison, 2035 Mechanical Engineering Building, 1513 University Avenue, Madison, WI, 53706, USA

    Arman Pazouki, Radu Serban & Dan Negrut

Authors
  1. Arman Pazouki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Radu Serban
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dan Negrut
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Arman Pazouki .

Editor information

Editors and Affiliations

  1. Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb, Croatia

    Zdravko Terze

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Pazouki, A., Serban, R., Negrut, D. (2014). A Lagrangian–Lagrangian Framework for the Simulation of Rigid and Deformable Bodies in Fluid. In: Terze, Z. (eds) Multibody Dynamics. Computational Methods in Applied Sciences, vol 35. Springer, Cham. https://doi.org/10.1007/978-3-319-07260-9_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-07260-9_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07259-3

  • Online ISBN: 978-3-319-07260-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation