Advertisement

Journal of Marine Science and Application

, Volume 16, Issue 4, pp 375–381 | Cite as

Monolithic coupling of the pressure and rigid body motion equations in computational marine hydrodynamics

  • Hrvoje Jasak
  • Inno Gatin
  • Vuko Vukčević
Article
  • 112 Downloads

Abstract

In Fluid Structure Interaction (FSI) problems encountered in marine hydrodynamics, the pressure field and the velocity of the rigid body are tightly coupled. This coupling is traditionally resolved in a partitioned manner by solving the rigid body motion equations once per nonlinear correction loop, updating the position of the body and solving the fluid flow equations in the new configuration. The partitioned approach requires a large number of nonlinear iteration loops per time–step. In order to enhance the coupling, a monolithic approach is proposed in Finite Volume (FV) framework, where the pressure equation and the rigid body motion equations are solved in a single linear system. The coupling is resolved by solving the rigid body motion equations once per linear solver iteration of the pressure equation, where updated pressure field is used to calculate new forces acting on the body, and by introducing the updated rigid body boundary velocity in to the pressure equation. In this paper the monolithic coupling is validated on a simple 2D heave decay case. Additionally, the method is compared to the traditional partitioned approach (i.e. “strongly coupled” approach) in terms of computational efficiency and accuracy. The comparison is performed on a seakeeping case in regular head waves, and it shows that the monolithic approach achieves similar accuracy with fewer nonlinear correctors per time–step. Hence, significant savings in computational time can be achieved while retaining the same level of accuracy.

Keywords

monolithic coupling pressure equation rigid body motion computational fluid dynamics marine hydrodynamics seakeeping 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

This research was sponsored by Bureau Veritas under the administration of Dr. Šime Malenica.

References

  1. Bna S, Manservisi S, Aulisa E, 2013. A multilevel domain decomposition solver for monolithic fluid-structure interaction problems. 11th International Conference of Numerical Analysis and Applied Mathematics 2013, Pts 1 and 2, Vol. 1558. Rhodes, 871–874. DOI: 10.1063/1.4825635Google Scholar
  2. Castiglione T, Stern F, Bova S, Kandasamy M, 2011. Numerical investigation of the seakeeping behavior of a catamaran advancing in regular head waves. Ocean Engineering, 38, 1806–1822. DOI: 10.1016/j.oceaneng.2011.09.003CrossRefGoogle Scholar
  3. Demirdžić I, Perić M, 1988. Space conservation law in finite volume calculations of fluid flow. International Journal for Numerical Methods in Fluids, 8(9), 1037–1050.MathSciNetCrossRefzbMATHGoogle Scholar
  4. Eken A, Sahin M, 2016. A parallel monolithic algorithm for the numerical simulation of large-scale fluid structure interaction problems. International Journal for Numerical Methods in Fluids, 80(12), 687–714. DOI: 10.1002/fld.4169MathSciNetCrossRefGoogle Scholar
  5. Farah P, Vuong AT, Wall WA, Popp A, 2016. Volumetric coupling approaches for multiphysics simulations on nonmatching meshes. International Journal for Numerical Methods in Engineering, 108(12), 1550–1576. DOI: 10.1002/nme.5285MathSciNetCrossRefGoogle Scholar
  6. Hachem E, Feghali S, Codina R, Coupez T, 2013. Immersed stress method for fluidstructure interaction using anisotropic mesh adaptation. International Journal for Numerical Methods in Engineering, 94(9), 805–825. DOI: 10.1002/nme.4481MathSciNetCrossRefzbMATHGoogle Scholar
  7. Heil M, Hazel AL, Boyle J, 2008. Solvers for large-displacement fluid-structure interaction problems: segregated versus monolithic approaches. Computational Mechanics, 43(1), 91–101. DOI: 10.1007/s00466-008-0270-6CrossRefzbMATHGoogle Scholar
  8. Hu Z, Tang WY, Xue HX, Zhang XY, 2016. A simple-based monolithic implicit method for strong-coupled fluid-structure interaction problems with free surfaces. Computer Methods in Applied Mechanics and Engineering, 299, 90–115. DOI: 10.1016/j.cma.2015.09.011MathSciNetCrossRefGoogle Scholar
  9. Irons BM, Tuck RC, 1969. A version of the Aitken accelerator for computer iteration. International Journal for Numerical Methods in Engineering, 1, 275–277. DOI: 10.1002/nme.1620010306CrossRefzbMATHGoogle Scholar
  10. Jasak H, 1996. Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College of Science, Technology & Medicine, London.Google Scholar
  11. Jasak H, Vukčević V, Gatin I, 2015. Numerical simulation of wave loads on static offshore structures. CFD for Wind and Tidal Offshore Turbines, 95–105.CrossRefGoogle Scholar
  12. Jog CS, Pal RK, 2011. A monolithic strategy for fluid-structure interaction problems. International Journal for Numerical Methods in Engineering, 85(4), 429–460. DOI: 10.1002/nme.2976MathSciNetCrossRefzbMATHGoogle Scholar
  13. Langer U, Yang HD, 2016. Robust and efficient monolithic fluid-structure-interaction solvers. International Journal for Numerical Methods in Engineering, 108(4), 303–325. DOI: 10.1002/nme.5214MathSciNetCrossRefGoogle Scholar
  14. Larsson L, Stern F, Visonneau M, Hirata N, Hino T, Kim J, 2015. Tokyo 2015: A Workshop on CFD in Ship Hydrodynamics. Vol. 3, NMRI (National Maritime Research Institute), Tokyo, Japan.Google Scholar
  15. Legay A, Zilian A, Janssen C, 2011. A rheological interface model and its space-time finite element formulation for fluid-structure interaction. International Journal for Numerical Methods in Engineering, 86(6), 667–687. DOI: 10.1002/nme.3060CrossRefzbMATHGoogle Scholar
  16. Miyata H, Orihara H, Sato Y, 2014. Nonlinear ship waves and computational fluid dynamics. Proceedings of the Japan Academy Series B—Physical and Biological Sciences, 90, 278–300. DOI: 10.2183/pjab.90.278CrossRefGoogle Scholar
  17. Orihara H, Miyata H, 2003. Evaluation of added resistance in regular incident waves by computational fluid dynamics motion simulation using an overlapping grid system. Journal of Marine Science and Technology, 8, 47–60. DOI: 10.1007/s00773-003-0163-5CrossRefGoogle Scholar
  18. Press WH, Teukolsky SA, Vetterling WT, Flannery BP, 2002. Numerical Recipes in C++: The Art of Scientific Computing. Cambridge University Press, Cambridge.zbMATHGoogle Scholar
  19. Robinson-Mosher A, Schroeder C, Fedkiw R, 2011. A symmetric positive definite formulation for monolithic fluid structure interaction. Journal of Computational Physics, 230(4), 1547–1566. DOI: 10.1016/j.jcp.2010.11.021MathSciNetCrossRefzbMATHGoogle Scholar
  20. Saad Y, 2003. Iterative methods for sparse linear systems. 2nd edition, Society for Industrial and Applied Mathematics Philadelphia.CrossRefzbMATHGoogle Scholar
  21. Simonsen CD, Otzen JF, Joncquez S, Stern F, 2013. EFD and CFD for KCS heaving and pitching in regular head waves. Journal of Marine Science and Technology, 18, 435–459. DOI: 10.1007/s00773-013-0219-0CrossRefGoogle Scholar
  22. Tezdogan T, Demirel YK, Kellett P, Khorasanchi M, Incecik A, Turan O, 2015. Full-scale unsteady RANS CFD simulations of ship behaviour and performance in head seas due to slow steaming. Ocean Engineering, 97, 186–206. DOI: 10.1016/j.oceaneng.2015.01.011CrossRefGoogle Scholar
  23. Vukčević V, 2016. Numerical modelling of coupled potential and viscous flow for marine applications. PhD thesis, Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb.Google Scholar
  24. Vukčević V, Jasak H, 2015a. Seakeeping validation and verification using decomposition model based on embedded free surface method. Tokyo 2015: A Workshop on CFD in Ship Hydrodynamics.Google Scholar
  25. Vukčević V, Jasak H, 2015b. Validation and verification of decomposition model based on embedded free surface method for oblique wave seakeeping simulations. Tokyo 2015: A Workshop on CFD in Ship Hydrodynamics.Google Scholar
  26. Vukčević V, Jasak H, Gatin I, Malenica S, 2016. Seakeeping sensitivity studies using the decomposition CFD model based on the ghost fluid method. Proceedings of the 31st Symposium on Naval Hydrodynamics, Monterey.Google Scholar
  27. Vukčević V, Jasak H, Malenica S, 2016a. Decomposition model for naval hydrodynamic applications, Part I: Computational method. Ocean Eng., 121, 37–46. DOI: 10.1016/j.oceaneng.2016.05.022CrossRefGoogle Scholar
  28. Vukčević V, Jasak H, Malenica S, 2016b. Decomposition model for naval hydrodynamic applications, Part II: Verification and validation. Ocean Eng., 121, 76–88. DOI: 10.1016/j.oceaneng.2016.05.021CrossRefGoogle Scholar
  29. Wu CS, Zhou DC, Gao L, Miao QM, 2011. CFD computation of ship motions and added resistance for a high speed trimaran in regular head waves. International Journal of Naval Architecture and Ocean Engineering, 3, 105–110. DOI: 10.3744/jnaoe.2011.3.1.105CrossRefGoogle Scholar
  30. Yang P, Xiang J, Fang F, Pavlidis D, Latham JP, Pain CC, 2016. Modelling of fluid-structure interaction with multiphase viscous flows using an immersed-body method. Journal of Computational Physics, 321, 571–592. DOI: 10.1016/j.jcp.2016.05.035MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Harbin Engineering University and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Faculty of Mechanical Engineering and Naval ArchitectureUniversity of ZagrebZagrebCroatia

Personalised recommendations