Skip to main content
Log in

A parallel interface tracking approach for evolving geometry problems

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

Abstract

This paper presents a parallel interface tracking approach for evolving geometry problems where both the computational domain and mesh are updated as dictated by the analysis. An interface-fitted conforming hybrid/mixed mesh with anisotropic layered elements is used. A combination of mesh motion and mesh modification is employed to update the mesh to account for the interface motion. Mesh modification is triggered only when necessary. During mesh motion and modification the desired structure, shape and resolution of the anisotropic layered elements at the interface are maintained. All steps are performed on partitioned meshes on distributed-memory parallel computers. The effectiveness of the current approach is demonstrated on two problems with large motion or deformation in the geometry.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

References

  1. Alauzet F, Li X, Seol ES, Shephard MS (2006) Parallel anisotropic 3D mesh adaptation by mesh modification. Eng Comput 21(3):247–258

    Article  Google Scholar 

  2. Anderson DM, McFadden GB, Wheeler AA (1998) Diffuse-interface methods in fluid mechanics. Annu Rev Fluid Mech 30(1):139–165

    Article  MathSciNet  MATH  Google Scholar 

  3. 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(2):397–422

    Article  Google Scholar 

  4. Batina JT (1990) Unsteady Euler airfoil solutions using unstructured dynamic meshes. AIAA J 28(8):1381–1388

    Article  Google Scholar 

  5. Boettinger WJ, Warren JA, Beckermann C, Karma A (2002) Phase-field simulation of solidification. Ann Rev Mater Res 32(1):163–194

    Article  Google Scholar 

  6. Breil J, Harribey T, Maire PH, Shashkov M (2013) A multi-material ReALE method with MOF interface reconstruction. Comput Fluids 83:115–125

    Article  MathSciNet  MATH  Google Scholar 

  7. Burg C (2004) A robust unstructured grid movement strategy using three-dimensional torsional springs. In: 34th AIAA Fluid dynamics conference and exhibit, p 2529

  8. Chessa J, Belytschko T (2003) An extended finite element method for two-phase fluids. J Appl Mech 70(1):10–17

    Article  MathSciNet  MATH  Google Scholar 

  9. Chitale KC, Sahni O, Shephard MS, Tendulkar S, Jansen KE (2014) Anisotropic adaptation for transonic flows with turbulent boundary layers. AIAA J 53(2):367–378

    Article  Google Scholar 

  10. Del Pino S (2011) Metric-based mesh adaptation for 2D Lagrangian compressible flows. J Comput Phys 230(5):1793–1821

    Article  MathSciNet  MATH  Google Scholar 

  11. Dobrev VA, Kolev TV, Rieben RN (2012) High-order curvilinear finite element methods for Lagrangian hydrodynamics. SIAM J Sci Comput 34(5):B606–B641

    Article  MathSciNet  MATH  Google Scholar 

  12. Donea J, Giuliani S, Halleux JP (1982) An arbitrary Lagrangian–Eulerian finite element method for transient dynamic fluid–structure interactions. Comput Methods Appl Mech Eng 33(1–3):689–723

    Article  MATH  Google Scholar 

  13. Dwight RP (2009) Robust mesh deformation using the linear elasticity equations. Comput Fluid Dyn 2006:401–406

    Google Scholar 

  14. Dyadechko V, Shashkov M (2008) Reconstruction of multi-material interfaces from moment data. J Comput Phys 227(11):5361–5384

    Article  MathSciNet  MATH  Google Scholar 

  15. Farhat C, Degand C, Koobus B, Lesoinne M (1998) Torsional springs for two-dimensional dynamic unstructured fluid meshes. Comput Methods Appl Mech Eng 163(1–4):231–245

    Article  MATH  Google Scholar 

  16. Fritts M, Boris J (1979) The Lagrangian solution of transient problems in hydrodynamics using a triangular mesh. J Comput Phys 31(2):173–215

    Article  MathSciNet  MATH  Google Scholar 

  17. Fyfe DE, Oran ES, Fritts M (1988) Surface tension and viscosity with Lagrangian hydrodynamics on a triangular mesh. J Comput Phys 76(2):349–384

    Article  MATH  Google Scholar 

  18. Garimella RV, Shephard MS (2000) Boundary layer mesh generation for viscous flow simulations. Int J Numer Methods Eng 49(1–2):193–218

    Article  MATH  Google Scholar 

  19. Glimm J, Grove JW, Li XL, Km Shyue, Zeng Y, Zhang Q (1998) Three-dimensional front tracking. SIAM J Sci Comput 19(3):703–727

    Article  MathSciNet  MATH  Google Scholar 

  20. Gropp W, Gropp WD, Lusk ADFEE, Lusk E, Skjellum A (1999) Using MPI: portable parallel programming with the message-passing interface, vol 1. MIT Press, Cambridge

    Book  MATH  Google Scholar 

  21. Guventurk C, Sahin M (2017) An arbitrary Lagrangian–Eulerian framework with exact mass conservation for the numerical simulation of 2D rising bubble problem. Int J Numer Methods Eng 112(13):2110–2134

    Article  MathSciNet  Google Scholar 

  22. Hassan O, Sørensen K, Morgan K, Weatherill N (2007) A method for time accurate turbulent compressible fluid flow simulation with moving boundary components employing local remeshing. Int J Numer Methods Fluids 53(8):1243–1266

    Article  MathSciNet  MATH  Google Scholar 

  23. Hauke G, Fuster D, Lizarraga F (2015) Variational multiscale a posteriori error estimation for systems: the Euler and Navier–Stokes equations. Comput Methods Appl Mech Eng 283:1493–1524

    Article  MathSciNet  MATH  Google Scholar 

  24. Hirt C, Amsden AA, Cook J (1974) An arbitrary Lagrangian–Eulerian computing method for all flow speeds. J Comput Phys 14(3):227–253

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  26. Hughes TJ, Liu WK, Zimmermann TK (1981) Lagrangian–Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29(3):329–349

    Article  MathSciNet  MATH  Google Scholar 

  27. Ibanez DA, Seol ES, Smith CW, Shephard MS (2016) PUMI: Parallel unstructured mesh infrastructure. ACM Trans Math Softw 42(3):17

    Article  MathSciNet  MATH  Google Scholar 

  28. Ibanez DA, Love E, Voth TE, Overfelt JR, Roberts NV, Hansen GA (2019) Tetrahedral mesh adaptation for Lagrangian shock hydrodynamics. Comput Math Appl 78(2):402–416

    Article  MathSciNet  MATH  Google Scholar 

  29. Ito Y, Nakahashi K (2002) Unstructured mesh generation for viscous flow computations. In: IMR, pp 367–377

  30. Jansen KE, Shephard MS, Beall MW (2001) On anisotropic mesh generation and quality control in complex flow problems. In: IMR, Citeseer

  31. Knupp P (2012) Introducing the target-matrix paradigm for mesh optimization via node-movement. Eng Comput 28(4):419–429

    Article  Google Scholar 

  32. Li X, Shephard MS, Beall MW (2005) 3D anisotropic mesh adaptation by mesh modification. Comput Methods Appl Mech Eng 194(48–49):4915–4950

    Article  MathSciNet  MATH  Google Scholar 

  33. Loubère R, Maire PH, Shashkov M, Breil J, Galera S (2010) Reale: a reconnection-based arbitrary-Lagrangian–Eulerian method. J Comput Phys 229(12):4724–4761

    Article  MathSciNet  MATH  Google Scholar 

  34. Nielsen EJ, Anderson WK (2002) Recent improvements in aerodynamic design optimization on unstructured meshes. AIAA J 40(6):1155–1163

    Article  Google Scholar 

  35. Osher S, Fedkiw RP (2001) Level set methods: an overview and some recent results. J Comput Phys 169(2):463–502

    Article  MathSciNet  MATH  Google Scholar 

  36. Peskin CS (2002) The immersed boundary method. Acta Numer 11:479–517

    Article  MathSciNet  MATH  Google Scholar 

  37. Quan S, Schmidt DP (2007) A moving mesh interface tracking method for 3D incompressible two-phase flows. J Comput Phys 221(2):761–780

    Article  MathSciNet  MATH  Google Scholar 

  38. Rodriguez JM, Sahni O, Lahey RT Jr, Jansen KE (2013) A parallel adaptive mesh method for the numerical simulation of multiphase flows. Comput Fluids 87:115–131

    Article  MathSciNet  MATH  Google Scholar 

  39. Sahni O, Jansen KE, Shephard MS, Taylor CA, Beall MW (2008) Adaptive boundary layer meshing for viscous flow simulations. Eng Comput 24(3):267–285

    Article  Google Scholar 

  40. Sahni O, Carothers CD, Shephard MS, Jansen KE (2009) Strong scaling analysis of a parallel, unstructured, implicit solver and the influence of the operating system interference. Sci Program 17(3):261–274

    Google Scholar 

  41. Sahni O, Zhou M, Shephard MS, Jansen KE (2009) Scalable implicit finite element solver for massively parallel processing with demonstration to 160k cores. In: Proceedings of the conference on high performance computing networking, storage and analysis, IEEE, pp 1–12

  42. Sahni O, Luo X, Jansen K, Shephard M (2010) Curved boundary layer meshing for adaptive viscous flow simulations. Finite Elem Anal Des 46(1):132–139

    Article  MathSciNet  Google Scholar 

  43. Sahni O, Ovcharenko A, Chitale KC, Jansen KE, Shephard MS (2017) Parallel anisotropic mesh adaptation with boundary layers for automated viscous flow simulations. Eng Comput 33(4):767–795

    Article  Google Scholar 

  44. Scardovelli R, Zaleski S (1999) Direct numerical simulation of free-surface and interfacial flow. Annu Rev Fluid Mech 31(1):567–603

    Article  MathSciNet  Google Scholar 

  45. Sethian JA, Smereka P (2003) Level set methods for fluid interfaces. Annu Rev Fluid Mech 35(1):341–372

    Article  MathSciNet  MATH  Google Scholar 

  46. Smith CW, Granzow B, Diamond G, Ibanez D, Sahni O, Jansen KE, Shephard MS (2018) In-memory integration of existing software components for parallel adaptive unstructured mesh workflows. Concurr Comp Pract E 30(18):e4510

    Article  Google Scholar 

  47. Stein K, Tezduyar TE, Benney R (2004) Automatic mesh update with the solid-extension mesh moving technique. Comput Methods Appl Mech Eng 193(21–22):2019–2032

    Article  MATH  Google Scholar 

  48. Sussman M, Smereka P, Osher S (1994) A level set approach for computing solutions to incompressible two-phase flow. J Comput Phys 114(1):146–159

    Article  MATH  Google Scholar 

  49. Tryggvason G, Bunner B, Esmaeeli A, Juric D, Al-Rawahi N, Tauber W, Han J, Nas S, Jan YJ (2001) A front-tracking method for the computations of multiphase flow. J Comput Phys 169(2):708–759

    Article  MathSciNet  MATH  Google Scholar 

  50. Wan J, Kocak S, Shephard MS (2005) Automated adaptive 3D forming simulation processes. Eng Comput 21(1):47–75

    Article  Google Scholar 

  51. Welch SW (1995) Local simulation of two-phase flows including interface tracking with mass transfer. J Comput Phys 121(1):142–154

    Article  MATH  Google Scholar 

  52. Yang Z, Mavriplis DJ (2007) Mesh deformation strategy optimized by the adjoint method on unstructured meshes. AIAA J 45(12):2885–2896

    Article  Google Scholar 

  53. Zeng D, Ethier CR (2005) A semi-torsional spring analogy model for updating unstructured meshes in 3D moving domains. Finite Elem Anal Des 41(11):1118–1139

    Article  Google Scholar 

  54. Zhang Y, Chandra A, Yang F, Shams E, Sahni O, Shephard M, Oberai AA (2019) A locally discontinuous ALE finite element formulation for compressible phase change problems. J Comput Phys 393:438–464

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work is supported by the U.S. Army Grants W911NF1410301 and W911NF16C0117.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Onkar Sahni.

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

Yang, F., Chandra, A., Zhang, Y. et al. A parallel interface tracking approach for evolving geometry problems. Engineering with Computers 38, 4289–4305 (2022). https://doi.org/10.1007/s00366-021-01386-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-021-01386-8

Keywords

Navigation