Skip to main content
Springer Nature Link
Log in

Non-manifold anisotropic mesh adaptation: application to fluid–structure interaction

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

A new strategy for high-fidelity unsteady mesh adaptation dealing with fluid–structure interaction (FSI) problems is presented using a partitioned approach. The Euler equations are solved by an edge-based Finite-Volume solver whereas the linear elasticity equations are solved by the finite-element method using the Lagrange \({\mathbb {P}}_1\) elements. The coupling between both codes is realized by imposing suitable boundary conditions on conforming meshes even at the fluid–structure interface. Small displacements of the structure are assumed and so the mesh is not deformed. The unsteady mesh adaptation process is based on a unique cavity operator which can handle non-manifold geometry, the fluid–structure interface in this work. The computation of a well-documented two-dimensional test case is finally carried out to perform validation of this new strategy as well as a three-dimensional test case to demonstrate our ability to treat complex three-dimensional test cases.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Garelli L, Paz R, Storti M (2010) Fluid–structure interaction study of the start-up of a rocket engine nozzle. Comput Fluids 39(7):1208

    Article  MATH  Google Scholar 

  2. Farhat C, Lesoinne M (2000) Two efficient staggered algorithms for the serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems. Comput Methods Appl Mech Eng 182(3–4):499

    Article  MATH  Google Scholar 

  3. Peskin C (1972) Flow patterns around heart valves: a numerical method. J Comput Phys 10(2):252

    Article  MathSciNet  MATH  Google Scholar 

  4. Formaggia L, Quarteroni A, Veneziani A (2009) Cardiovascular mathematics: modeling and simulation of the circulatory system, vol 1. Springer-Modelling, Simulations and Applications, New York

    Book  MATH  Google Scholar 

  5. Astorino M, Chouly F, Fernández M (2010) Robin based semi-implicit coupling in fluid-structure interaction: stability analysis and numerics. SIAM J Sci Comput 31(6):4041

    Article  MathSciNet  MATH  Google Scholar 

  6. Alauzet F, Loseille A (2016) A decade of progress on anisotropic mesh adaptation for computational fluid dynamics. Comput Aided Des 72:13

    Article  MathSciNet  Google Scholar 

  7. Alauzet F, Loseille A (2010) High order sonic boom modeling by adaptive methods. J Comput Phys 229:561

    Article  MathSciNet  MATH  Google Scholar 

  8. Alauzet F, Frazza L (2019) 3D RANS anisotropic mesh adaptation on the high-lift version of NASA’s Common Research Model (HL-CRM), In: 25th AIAA Fluid Dynamics Conference (AIAA Paper 2019–2947. Dallas, TX, USA

  9. Langenhove JV, Lucor D, Alauzet F, Belme A (2018) Goal-oriented error control of stochastic system approximations using metric-based anisotropic adaptations. J Comput Phys 374:384

    Article  MathSciNet  MATH  Google Scholar 

  10. Amari T, Canou A, Aly JJ, Delyon F, Alauzet F (2018) Magnetic cage and rope as the key for solar eruptions. Nature 554:211

    Article  Google Scholar 

  11. Guégan D, Allain O, Dervieux A, Alauzet F (2010) An \({L}^\infty \)-\({L}^p\) mesh adaptive method for computing unsteady bi-fluid flows. Int J Numer Methods Eng 84(11):1376

    Article  MATH  Google Scholar 

  12. Alauzet F, Loseille A, Olivier G (2018) Time-accurate multi-scale anisotropic mesh adaptation for unsteady flows in CFD. J Comput Phys 373:28

    Article  MathSciNet  MATH  Google Scholar 

  13. Alauzet F (2014) A changing-topology moving mesh technique for large displacement. Eng Comput 30(2):175

    Article  Google Scholar 

  14. Barral N, Olivier G, Alauzet F (2017) Metric-based anisotropic mesh adaptation for three-dimensional time-dependent problems involving moving geometries. J Comput Phys 331:157

    Article  MathSciNet  MATH  Google Scholar 

  15. Vanharen J, Puigt G, Montagnac M (2015) Theoretical and numerical analysis of nonconforming grid interface for unsteady flows. J Comput Phys 285:111

    Article  MathSciNet  MATH  Google Scholar 

  16. Loseille A, Löhner R (2013) Cavity-based operators for mesh adaptation. In: 51th AIAA Aerospace Sciences Meeting (AIAA Paper 2013–0152. Dallas, TX, USA

  17. Loseille A, Alauzet F, Menier V (2017) Unique cavity-based operator and hierarchical domain partitioning for fast parallel generation of anisotropic meshes. Comput Aided Des 85:53

    Article  Google Scholar 

  18. Vanharen J, Feuillet R, Alauzet F (2018) Mesh adaptation for fluid-structure interaction problems. In: 24th AIAA Fluid Dynamics Conference (AIAA Paper 2018–3244. Atlanta, GA, USA

  19. Alauzet F (2010) Size gradation control of anisotropic meshes. Finite Elem Anal Des 46:181

    Article  MathSciNet  Google Scholar 

  20. Felker F (1993) Direct solution of two-dimensional Navier-Stokes equations for static aeroelasticity problems. AIAA J 31(1):148

    Article  MATH  Google Scholar 

  21. Blom F (1998) A monolithical fluid-structure interaction algorithm applied to the piston problem. Comput Methods Appl Mech Eng 167(3–4):369

    Article  MathSciNet  MATH  Google Scholar 

  22. Soria A, Casadei F (1997) Arbitrary Lagrangian-Eulerian multicomponent compressible flow with fluid-structure interaction. Int J Numer Methods Fluids 25(11):1263

    Article  MATH  Google Scholar 

  23. Rifai S, Johan Z, Wang WP, Grisval JP, Hughes T, Ferencz R (1999) Multiphysics simulation of flow-induced vibrations and aeroelasticity on parallel computing platforms. Comput Methods Appl Mech Eng 174(3–4):393

    Article  MathSciNet  MATH  Google Scholar 

  24. Farhat C, Lesoinne M, Maman N (1995) Mixed explicit/implicit time integration of coupled aeroelastic problems: three-field formulation, geometric conservation and distributed solution. Int J Numer Methods Fluids 21(10):807

    Article  MathSciNet  MATH  Google Scholar 

  25. Cebral J, Löhner R (1997) Conservative load projection and tracking for fluid-structure problems. AIAA J 35(4):687

    Article  MATH  Google Scholar 

  26. Giordano J, Jourdan G, Burtschell Y, Medale M, Zeitoun DE, Houas L (2005) Shock wave impacts on deforming panel, an application of fluid-structure interaction. Shock Waves 14(1–2):103

    Article  MATH  Google Scholar 

  27. Sanches R, Coda H (2014) On fluid–shell coupling using an arbitrary Lagrangian-Eulerian fluid solver coupled to a positional Lagrangian shell solver. Appl Math Model 38(14):3401

    Article  MathSciNet  MATH  Google Scholar 

  28. Pasquariello V, Hammerl G, Örley F, Hickel S, Danowski C, Popp A, Wall W, Adams N (2016) A cut-cell finite volume—finite element coupling approach for fluid–structure interaction in compressible flow. J Comput Phys 307:670

    Article  MathSciNet  MATH  Google Scholar 

  29. Debiez C, Dervieux A, Mer K, Nkonga B (1998) Computation of unsteady flows with mixed finite volume/finite element upwind methods. Int J Numer Methods Fluids 27(1–4):193

    Article  MathSciNet  MATH  Google Scholar 

  30. Cournède PH, Koobus B, Dervieux A (2006) Positivity statements for a mixed-element-volume scheme on fixed and moving grids. Revue Eur Mec Numer 15(7–8):767

    MATH  Google Scholar 

  31. Toro E, Spruce M, Speares W (1994) Restoration of the contact surface in the HLL-Riemann solver. Shock Waves 4(1):25

    Article  MATH  Google Scholar 

  32. Shu CW, Osher S (1988) Efficient implementation of essentially non-oscillatory shock-capturing schemes. J Comput Phys 77(2):439

    Article  MathSciNet  MATH  Google Scholar 

  33. Spiteri R, Ruuth S (2002) A new class of optimal high-order strong-stability-preserving time discretization methods. SIAM J Numer Anal 40(2):469

    Article  MathSciNet  MATH  Google Scholar 

  34. Newmark N (1959) A method of computation for structural dynamics. J Eng Mech Div 85(3):67–94

    Article  Google Scholar 

  35. Loseille A, Alauzet F (2011) Continuous mesh framework. Part I: well-posed continuous interpolation error. SIAM J Numer Anal 49(1):38

    Article  MathSciNet  MATH  Google Scholar 

  36. Loseille A, Alauzet F (2011) Continuous mesh framework. Part II: validations and applications. SIAM J Numer Anal 49(1):61

    Article  MathSciNet  MATH  Google Scholar 

  37. Alauzet F, Frey P, George P, Mohammadi B (2007) 3D transient fixed point mesh adaptation for time-dependent problems: application to CFD simulations. J Comput Phys 222:592

    Article  MathSciNet  MATH  Google Scholar 

  38. Olivier G (2011) Anisotropic metric-based mesh adaptation for unsteady CFD simulations involving moving geometries. Ph.D. thesis, Université Pierre et Marie Curie, Paris VI, Paris, France

  39. Loseille A, Alauzet F (2009) Optimal 3D highly anisotropic mesh adaptation based on the continuous mesh framework, In: Proceedings of the 18th International Meshing Roundtable (Springer, 2009), pp 575–594

  40. Alauzet F (2016) A parallel matrix-free conservative solution interpolation on unstructured tetrahedral meshes. Comput Methods Appl Mech Eng 299:116

    Article  MathSciNet  MATH  Google Scholar 

  41. Loseille A (2017) Chapter 10—Unstructured mesh generation and adaptation. In: Abgrall R, Shu C-W (eds) Handbook of numerical methods for hyperbolic problems — applied and modern issues, vol 18. Elsevier, pp 263–302. https://doi.org/10.1016/bs.hna.2016.10.004

  42. Loseille A, Menier V (2013) Serial and parallel mesh modification through a unique cavity-based primitive. In: Proceedings of the 22th International Meshing Roundtable (Springer, 2013), pp 541–558

  43. Frey P (2000) About surface remeshing. In: Proceedings of the 9th International Meshing Roundtable (New Orleans, LO, USA, 2000), pp 123–136

  44. Loseille A, Feuillet R (2018) Vizir: high-order mesh and solution visualization using OpenGL 4.0 graphic pipeline, In: 2018 AIAA Aerospace Sciences Meeting, 2018

  45. Barral N, Alauzet F (2019) Three-dimensional CFD simulations with large displacement of the geometries using a connectivity-change moving mesh approach. Eng Comput 35:397

    Article  Google Scholar 

Download references

Acknowledgements

The development of the structure solver and the multi-physics error estimates and strategy was supported by a RAPID DGA program. The development of the non-manifold mesh adaptation is supported by ANR IMPACTS (ANR-18-CE46-0003).

Author information

Authors and Affiliations

  1. Gamma Project, Inria Saclay, Île-de-France, 91120, Palaiseau, France

    Julien Vanharen, Adrien Loseille & Frédéric Alauzet

Authors
  1. Julien Vanharen
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Adrien Loseille
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Frédéric Alauzet
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Adrien Loseille.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vanharen, J., Loseille, A. & Alauzet, F. Non-manifold anisotropic mesh adaptation: application to fluid–structure interaction. Engineering with Computers 38, 4269–4288 (2022). https://doi.org/10.1007/s00366-021-01435-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-021-01435-2

Keywords