Skip to main content
SpringerLink
Log in

Leveraging code generation for transparent immersogeometric fluid–structure interaction analysis on deforming domains

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

Abstract

Code generation technology has been transformative to the field of numerical partial differential equations (PDEs), allowing domain scientists and engineers to automatically compile high-performance solver routines from abstract mathematical descriptions of PDE systems. However, this often assumes a rigid code structure, which is only appropriate to a subset of applications and numerical methods, such as the traditional finite element methods used by the FEniCS code generation system. The present contribution demonstrates how to productively integrate FEniCS into a custom implementation of immersogeometric analysis (IMGA) of thin shell structures interacting with incompressible fluid flows on deforming domains. IMGA is an emerging paradigm for numerical PDEs with complex domain geometries, where non-watertight geometry descriptions are used directly as computational meshes. In particular, we generalize past related work by leveraging code generation to concisely pull back the deforming-domain Navier–Stokes problem to a stationary reference mesh. We also show how code generation enables rapid implementation of different material models for the structure subproblem. We verify our implementation using several benchmark problems, demonstrate its robustness and flexibility by simulating a prosthetic heart valve immersed in a flexible artery, and distribute the full source code online, to be used and modified by the community. Impact of the last item is amplified by the transparent nature of our code-generation-based implementation.

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

Access this article

Log in via an institution

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
Fig. 12

Similar content being viewed by others

Notes

  1. We shall not attempt to review all recent work on heart valve FSI here, as this (substantial) task is already accomplished by dedicated review articles [26,27,28]; our introduction is limited to direct ancestors of the present contribution.

  2. We interpret the adjective “immersed” rather liberally here, using it to refer to any numerical method in which a computational mesh is not fitted to a boundary or interface; this is at odds with some references, which reserve it for a specific method introduced by [31].

  3. This is in contrast with the shell structure subproblem, where we consider incompressible material in some problems, to model biological soft tissue in heart valve leaflets. One might (correctly) point out that a high-fidelity model of arterial soft tissue should also be incompressible, but the scope of our solid artery modeling is limited to capturing its effect on valve dynamics; this does not depend critically on details of the artery’s constitutive model.

  4. This mathematical result of course contradicts everyday experience; the principled solution is to consider the interaction of flow with surface roughness, as detailed in [48], but we proceed with a practical ad hoc approach in the present work.

  5. A factor of \(h_\text {th}^2\) has been absorbed into the potential density \(\phi \), to account for the difference between area integrals here and volume integrals in [49, (17)].

  6. By default, convergence is tested by computing \(\ell ^2\) norms of assembled residual vectors for both the fluid–solid and shell subproblems, normalizing these against residual norms computed at the start of the iteration, and checking whether both fall below a given relative tolerance.

  7. A variant with leaflet coaptation is documented in [58].

  8. Although blood flow has well-documented non-Newtonian features, the Newtonian model remains appropriate in large arteries [94].

  9. For a detailed explanation of the mechanism behind this flow rate oscillation, see the electrical circuit analogy used to discuss results in [21, Section 5.4.4].

  10. This repository state can always be recovered using Git, but we expect post-publication changes to improve the software, and recommend against reverting to previous states for most practical purposes.

References

  1. Johnson C (2012) Numerical solution of partial differential equations by the finite element method. Dover books on mathematics series. Dover Publications, Sweden

    Google Scholar 

  2. Logg A, Mardal K-A, Wells GN et al (2012) Automated solution of differential equations by the finite element method. Springer, Switzerland

    MATH  Google Scholar 

  3. Alnæs MS, Logg A, Ølgaard KB, Rognes ME, Wells GN (2014) Unified form language: a domain-specific language for weak formulations of partial differential equations. ACM Trans Math Softw 40(2):9–1937

    MathSciNet  MATH  Google Scholar 

  4. Kirby RC, Logg A (2006) A compiler for variational forms. ACM Trans Math Softw 32(3):417–444

    MathSciNet  Google Scholar 

  5. Logg A, Wells GN (2010) DOLFIN: automated finite element computing. ACM Trans Math Softw 37(2):1–28

    MathSciNet  MATH  Google Scholar 

  6. Evans JA, Kamensky D, Bazilevs Y (2020) Variational multiscale modeling with discretely divergence-free subscales. Comput Math Appl 80(11):2517–2537

    MathSciNet  MATH  Google Scholar 

  7. Calo VM, Ern A, Muga I, Rojas S (2020) An adaptive stabilized conforming finite element method via residual minimization on dual discontinuous Galerkin norms. Comput Methods Appl Mech Eng 363:112891

    MathSciNet  MATH  Google Scholar 

  8. Medina E, Farrell PE, Bertoldi K, Rycroft CH (2020) Navigating the landscape of nonlinear mechanical metamaterials for advanced programmability. Phys Rev B 101:064101

    Google Scholar 

  9. Carlson J, Pack A, Transtrum MK, Lee J, Seidman DN, Liarte DB, Sitaraman NS, Senanian A, Kelley MM, Sethna JP, Arias T, Posen S (2021) Analysis of magnetic vortex dissipation in Sn-segregated boundaries in Nb3Sn superconducting RF cavities. Phys Rev B 103:024516

    Google Scholar 

  10. Hoffman J, Jansson J, Johnson C (2016) New theory of flight. J Math Fluid Mech 18(2):219–241

    MathSciNet  MATH  Google Scholar 

  11. Jansson J, Krishnasamy E, Leoni M, Jansson N, Hoffman J (2018). In: López Mejia OD, Escobar Gomez JA (eds) Time-resolved adaptive direct FEM simulation of high-lift aircraft configurations, pp 67–92. Springer, Switzerland

  12. Petras A, Leoni M, Guerra JM, Jansson J, Gerardo-Giorda L (2018) Effect of tissue elasticity in cardiac radiofrequency catheter ablation models. 2018 Comput Cardiol Conf (CinC) 45:1–4

    Google Scholar 

  13. Richardson CN, Sime N, Wells GN (2019) Scalable computation of thermomechanical turbomachinery problems. Finite Elem Anal Des 155:32–42

    Google Scholar 

  14. LeVeque RJ, Mitchell IM, Stodden V (2012) Reproducible research for scientific computing: tools and strategies for changing the culture. Comput Sci Eng 14(4):13–17

    Google Scholar 

  15. Ivie P, Thain D (2018) Reproducibility in scientific computing. ACM Comput Surv 51(3)

  16. Scott LR (2018) Introduction to automated modeling with FEniCS. Computational Modeling Initiative LLC, Chicago

    Google Scholar 

  17. Angoshtari A, Matin AG (2020) Finite element methods in civil and mechanical engineering. CRC Press, Boca Raton

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  19. Mittal R, Iaccarino G (2005) Immersed boundary methods. Annu Rev Fluid Mech 37:239–261

    MathSciNet  MATH  Google Scholar 

  20. Chen J-S, Hillman M, Chi S-W (2017) Meshfree methods: progress made after 20 years. J Eng Mech 143(4):04017001

    Google Scholar 

  21. Kamensky D, Hsu M-C, Schillinger D, Evans JA, Aggarwal A, Bazilevs Y, Sacks MS, Hughes TJR (2015) An immersogeometric variational framework for fluid-structure interaction: application to bioprosthetic heart valves. Comput Methods Appl Mech Eng 284:1005–1053

    MathSciNet  MATH  Google Scholar 

  22. Hsu M-C, Kamensky D, Bazilevs Y, Sacks MS, Hughes TJR (2014) Fluid-structure interaction analysis of bioprosthetic heart valves: significance of arterial wall deformation. Comput Mech 54:1055–1071

    MathSciNet  MATH  Google Scholar 

  23. Hsu M-C, Kamensky D, Xu F, Kiendl J, Wang C, Wu MCH, Mineroff J, Reali A, Bazilevs Y, Sacks MS (2015) Dynamic and fluid-structure interaction simulations of bioprosthetic heart valves using parametric design with T-splines and Fung-type material models. Comput Mech 55:1211–1225

    MATH  Google Scholar 

  24. Kamensky D, Hsu M-C, Yu Y, Evans JA, Sacks MS, Hughes TJR (2017) Immersogeometric cardiovascular fluid-structure interaction analysis with divergence-conforming B-splines. Comput Methods Appl Mech Eng 314:408–472

    MathSciNet  MATH  Google Scholar 

  25. Xu F, Morganti S, Zakerzadeh R, Kamensky D, Auricchio F, Reali A, Hughes TJR, Sacks MS, Hsu M-C (2018) A framework for designing patient-specific bioprosthetic heart valves using immersogeometric fluid-structure interaction analysis. Int J Numer Methods Biomed Eng 34(4):2938

    MathSciNet  Google Scholar 

  26. Borazjani I (2015) A review of fluid-structure interaction simulations of prosthetic heart valves. J Long Term Eff Med Implants 25(1–2):75–93

    Google Scholar 

  27. Hirschhorn M, Tchantchaleishvili V, Stevens R, Rossano J, Throckmorton A (2020) Fluid-structure interaction modeling in cardiovascular medicine—a systematic review 2017–2019. Med Eng Phys 78:1–13

    Google Scholar 

  28. Abbas SS, Nasif MS, Al-Waked R (2022) State-of-the-art numerical fluid-structure interaction methods for aortic and mitral heart valves simulations: a review. Simulation 98(1):3–34

    Google Scholar 

  29. Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput Methods Appl Mech Eng 194:4135–4195

    MathSciNet  MATH  Google Scholar 

  30. Cottrell JA, Hughes TJR, Bazilevs Y (2009) Isogeometric analysis: toward integration of CAD and FEA. Wiley, Chichester

    MATH  Google Scholar 

  31. Peskin CS (1972) Flow patterns around heart valves: a numerical method. J Comput Phys 10(2):252–271

    MathSciNet  MATH  Google Scholar 

  32. Kamensky D (2021) Open-source immersogeometric analysis of fluid-structure interaction using FEniCS and tIGAr. Comput Math Appl 81:634–648

    MathSciNet  MATH  Google Scholar 

  33. https://github.com/david-kamensky/CouDALFISh: CouDALFISh source code

  34. Kamensky D, Bazilevs Y (2019) tIGAr: automating isogeometric analysis with FEniCS. Comput Methods Appl Mech Eng 344:477–498

    MathSciNet  MATH  Google Scholar 

  35. Donea J, Huerta A, Ponthot J-P, Rodriguez-Ferran A (2004) Arbitrary Lagrangian–Eulerian methods. In: Encyclopedia of Computational Mechanics. Volume 3: Fluids. John Wiley & Sons, Hoboken, New Jersey. Chap. 14

  36. Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid-structure interaction: theory, algorithms, and computations. Comput Mech 43:3–37

    MathSciNet  MATH  Google Scholar 

  37. Esmaily-Moghadam M, Bazilevs Y, Hsia T-Y, Vignon-Clementel IE, Marsden AL, of Congenital Hearts Alliance (MOCHA), M (2011) A comparison of outlet boundary treatments for prevention of backflow divergence with relevance to blood flow simulations. Comput Mech 48:277–291

    MathSciNet  MATH  Google Scholar 

  38. Bazilevs Y, Calo VM, Cottrel JA, Hughes TJR, Reali A, Scovazzi G (2007) Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Comput Methods Appl Mech Eng 197:173–201

    MathSciNet  MATH  Google Scholar 

  39. Akkerman I, Bazilevs Y, Calo VM, Hughes TJR, Hulshoff S (2008) The role of continuity in residual-based variational multiscale modeling of turbulence. Comput Mech 41:371–378

    MathSciNet  MATH  Google Scholar 

  40. Bazilevs Y, Michler C, Calo VM, Hughes TJR (2010) Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes. Comput Methods Appl Mech Eng 199:780–790

    MathSciNet  MATH  Google Scholar 

  41. Takizawa K, Bazilevs Y, Tezduyar TE (2012) Space-time and ALE-VMS techniques for patient-specific cardiovascular fluid-structure interaction modeling. Arch Comput Methods Eng 19:171–225

    MathSciNet  MATH  Google Scholar 

  42. Bazilevs Y, Hsu M-C, Takizawa K, Tezduyar TE (2012) ALE-VMS and ST-VMS methods for computer modeling of wind-turbine rotor aerodynamics and fluid-structure interaction. Math Models Methods Appl Sci 22:1230002

    MATH  Google Scholar 

  43. Hsu M-C, Akkerman I, Bazilevs Y (2014) Finite element simulation of wind turbine aerodynamics: validation study using NREL Phase VI experiment. Wind Energy

  44. Korobenko A, Hsu M-C, Akkerman I, Bazilevs Y (2014) Aerodynamic simulation of vertical-axis wind turbines. J Appl Mech 81:021011

    Google Scholar 

  45. Takizawa K, Bazilevs Y, Tezduyar TE, Long CC, Marsden AL, Schjodt K (2014) ST and ALE-VMS methods for patient-specific cardiovascular fluid mechanics modeling. Math Models Methods Appl Sci 24:2437–2486

    MathSciNet  MATH  Google Scholar 

  46. Kiendl J, Hsu M-C, Wu MCH, Reali A (2015) Isogeometric Kirchhoff-Love shell formulations for general hyperelastic materials. Comput Methods Appl Mech Eng 291:280–303

    MathSciNet  MATH  Google Scholar 

  47. Kiendl J, Bletzinger K-U, Linhard J, Wüchner R (2009) Isogeometric shell analysis with Kirchhoff-Love elements. Comput Methods Appl Mech Eng 198:3902–3914

    MathSciNet  MATH  Google Scholar 

  48. Ager C, Schott B, Vuong A-T, Popp A, Wall WA (2019) A consistent approach for fluid-structure-contact interaction based on a porous flow model for rough surface contact. Int J Numer Meth Eng 119(13):1345–1378

    MathSciNet  Google Scholar 

  49. Kamensky D, Xu F, Lee C-H, Yan J, Bazilevs Y, Hsu M-C (2018) A contact formulation based on a volumetric potential: application to isogeometric simulations of atrioventricular valves. Comput Methods Appl Mech Eng 330:522–546

    MathSciNet  MATH  Google Scholar 

  50. Belytschko T, Neal MO (1991) Contact-impact by the pinball algorithm with penalty and Lagrangian methods. Int J Numer Meth Eng 31(3):547–572

    MATH  Google Scholar 

  51. Kamensky D, Behzadinasab M, Foster JT, Bazilevs Y (2019) Peridynamic modeling of frictional contact. J Peridyn Nonlocal Model 1(2):107–121

    MathSciNet  Google Scholar 

  52. Kamensky D, Alaydin MD, Bazilevs Y (2022) A review of nonlocality in computational contact mechanics. In: Aldakheel F, Hudobivnik B, Soleimani M, Wessels H, Weißenfels C, Marino M (eds) Current trends and open problems in computational mechanics. Springer, Cham, pp 239–246

    MATH  Google Scholar 

  53. Bazilevs Y, Takizawa K, Tezduyar TE (2013) Computational fluid-structure interaction: methods and applications. Wiley, Chichester

    MATH  Google Scholar 

  54. Tezduyar T, Aliabadi S, Behr M, Johnson A, Mittal S (1993) Parallel finite-element computation of 3D flows. Computer 26(10):27–36

    MATH  Google Scholar 

  55. Johnson AA, Tezduyar TE (1994) Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces. Comput Methods Appl Mech Eng 119:73–94

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  57. Stein K, Tezduyar T, Benney R (2003) Mesh moving techniques for fluid-structure interactions with large displacements. J Appl Mech 70:58–63

    MATH  Google Scholar 

  58. Kamensky D, Evans JA, Hsu M-C (2015) Stability and conservation properties of collocated constraints in immersogeometric fluid-thin structure interaction analysis. Commun Comput Phys 18:1147–1180

    MathSciNet  MATH  Google Scholar 

  59. Hsu M-C, Kamensky D (2018) Immersogeometric analysis of bioprosthetic heart valves, using the dynamic augmented Lagrangian method. In: Tezduyar TE (ed) Frontiers in computational fluid-structure interaction and flow simulation. Springer, Cham, pp 167–212

    Google Scholar 

  60. van Brummelen EH (2009) Added mass effects of compressible and incompressible flows in fluid-structure interaction. J Appl Mech 76:021206

    Google Scholar 

  61. Chung J, Hulbert GM (1993) A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-\(\alpha \) method. J Appl Mech 60:371–75

    MathSciNet  MATH  Google Scholar 

  62. Jansen KE, Whiting CH, Hulbert GM (2000) A generalized-\(\alpha \) method for integrating the filtered Navier-Stokes equations with a stabilized finite element method. Comput Methods Appl Mech Eng 190:305–319

    MathSciNet  MATH  Google Scholar 

  63. Kamensky D, Evans JA, Hsu M-C, Bazilevs Y (2017) Projection-based stabilization of interface Lagrange multipliers in immersogeometric fluid-thin structure interaction analysis, with application to heart valve modeling. Comput Math Appl 74(9):2068–2088

    MathSciNet  MATH  Google Scholar 

  64. Yu Y, Kamensky D, Hsu M-C, Lu XY, Bazilevs Y, Hughes TJR (2018) Error estimates for projection-based dynamic augmented Lagrangian boundary condition enforcement, with application to fluid-structure interaction. Math Models Methods Appl Sci 28(12):2457–2509

    MathSciNet  MATH  Google Scholar 

  65. John V, Linke A, Merdon C, Neilan M, Rebholz L (2017) On the divergence constraint in mixed finite element methods for incompressible flows. SIAM Rev 59(3):492–544

    MathSciNet  MATH  Google Scholar 

  66. Casquero H, Bona-Casas C, Gomez H (2017) NURBS-based numerical proxies for red blood cells and circulating tumor cells in microscale blood flow. Comput Methods Appl Mech Eng 316:646–667

    MathSciNet  MATH  Google Scholar 

  67. Boilevin-Kayl L, Fernández MA, Gerbeau J-F (2019) Numerical methods for immersed FSI with thin-walled structures. Comput Fluids 179:744–763

    MathSciNet  MATH  Google Scholar 

  68. Boilevin-Kayl L, Fernández M, Gerbeau J-F (2019) A loosely coupled scheme for fictitious domain approximations of fluid-structure interaction problems with immersed thin-walled structures. SIAM J Sci Comput 41(2):351–374

    MathSciNet  MATH  Google Scholar 

  69. Casquero H, Zhang YJ, Bona-Casas C, Dalcin L, Gomez H (2018) Non-body-fitted fluid-structure interaction: divergence-conforming B-splines, fully-implicit dynamics, and variational formulation. J Comput Phys 374:625–653

    MathSciNet  MATH  Google Scholar 

  70. Casquero H, Bona-Casas C, Toshniwal D, Hughes TJR, Gomez H, Zhang YJ (2021) The divergence-conforming immersed boundary method: application to vesicle and capsule dynamics. J Comput Phys 425:109872

    MathSciNet  MATH  Google Scholar 

  71. Tong GG, Kamensky D, Evans JA (2022) Skeleton-stabilized divergence-conforming B-spline discretizations for incompressible flow problems of high Reynolds number. Comput Fluids 248:105667

    MathSciNet  MATH  Google Scholar 

  72. https://github.com/david-kamensky/ShNAPr: ShNAPr source code

  73. https://github.com/david-kamensky/VarMINT: VarMINT source code

  74. Tezduyar TE, Sathe S (2007) Modelling of fluid-structure interactions with the space-time finite elements: solution techniques. Int J Numer Meth Fluids 54(6–8):855–900

    MathSciNet  MATH  Google Scholar 

  75. Taylor GI (1923) On the decay of vortices in a viscous fluid. Lond Edinburgh Dublin Philos Magazine J Sci 46(274):671–674

    MATH  Google Scholar 

  76. Turek S, Hron J (2006) Proposal for numerical benchmarking of fluid-structure interaction between an elastic object and laminar incompressible flow. In: Bungartz H-J, Schäfer M (eds) Fluid-structure interaction. Springer, Berlin, pp 371–385

    MATH  Google Scholar 

  77. Turek S, Hron J, Razzaq M, Wobker H, Schäfer M (2010) Numerical benchmarking of fluid-structure interaction: a comparison of different discretization and solution approaches. In: Bungartz H-J, Mehl M, Schäfer M (eds) Fluid structure interaction II. Springer, Berlin, pp 413–424

    MATH  Google Scholar 

  78. Tian F-B, Dai H, Luo H, Doyle JF, Rousseau B (2014) Fluid-structure interaction involving large deformations: 3D simulations and applications to biological systems. J Comput Phys 258:451–469

    MathSciNet  MATH  Google Scholar 

  79. Mehl M, Uekermann B, Bijl H, Blom D, Gatzhammer B, van Zuijlen A (2016) Parallel coupling numerics for partitioned fluid-structure interaction simulations. Comput Math Appl 71(4):869–891

    MathSciNet  MATH  Google Scholar 

  80. Bungartz H-J, Lindner F, Gatzhammer B, Mehl M, Scheufele K, Shukaev A, Uekermann B (2016) Precice—a fully parallel library for multi-physics surface coupling. Comput Fluids 141:250–258

    MathSciNet  MATH  Google Scholar 

  81. Heil M, Hazel AL, Boyle J (2008) Solvers for large-displacement fluid-structure interaction problems: segregated versus monolithic approaches. Comput Mech 43:91–101

    MATH  Google Scholar 

  82. Breuer M, De Nayer G, Münsch M, Gallinger T, Wüchner R (2012) Fluid-structure interaction using a partitioned semi-implicit predictor-corrector coupling scheme for the application of large-eddy simulation. J Fluids Struct 29:107–130

    Google Scholar 

  83. Geuzaine C, Remacle J-F (2009) Gmsh: a 3-D finite element mesh generator with built-in pre- and post-processing facilities. Int J Numer Meth Eng 79(11):1309–1331

    MathSciNet  MATH  Google Scholar 

  84. a MUltifrontal Massively Parallel sparse direct Solver, M.: http://mumps.enseeiht.fr/. Accessed 24 Apr 2016

  85. Bazilevs Y, Hsu M-C, Scott MA (2012) Isogeometric fluid-structure interaction analysis with emphasis on non-matching discretizations, and with application to wind turbines. Comput Methods Appl Mech Eng 249–252:28–41

    MathSciNet  MATH  Google Scholar 

  86. Hesch C, Gil AJ, Arranz Carreño A, Bonet J (2012) On continuum immersed strategies for fluid-structure interaction. Comput Methods Appl Mech Eng 247–248:51–64

    MathSciNet  MATH  Google Scholar 

  87. Gil AJ, Carreño AA, Bonet J, Hassan O (2013) An enhanced immersed structural potential method for fluid-structure interaction. J Comput Phys 250:178–205

    MathSciNet  MATH  Google Scholar 

  88. Wick T (2014) Flapping and contact FSI computations with the fluid-solid interface-tracking/interface-capturing technique and mesh adaptivity. Comput Mech 53(1):29–43

    MathSciNet  MATH  Google Scholar 

  89. Wu MCH, Zakerzadeh R, Kamensky D, Kiendl J, Sacks MS, Hsu M-C (2018) An anisotropic constitutive model for immersogeometric fluid-structure interaction analysis of bioprosthetic heart valves. J Biomech 74:23–31

    Google Scholar 

  90. Wu MCH, Muchowski HM, Johnson EL, Rajanna MR, Hsu M-C (2019) Immersogeometric fluid-structure interaction modeling and simulation of transcatheter aortic valve replacement. Comput Methods Appl Mech Eng 357:112556

    MathSciNet  MATH  Google Scholar 

  91. Johnson EL, Wu MCH, Xu F, Wiese NM, Rajanna MR, Herrema AJ, Ganapathysubramanian B, Hughes TJR, Sacks MS, Hsu M-C (2020) Thinner biological tissues induce leaflet flutter in aortic heart valve replacements. Proc Natl Acad Sci 117(32):19007–19016

    Google Scholar 

  92. Xu F, Johnson EL, Wang C, Jafari A, Yang C-H, Sacks MS, Krishnamurthy A, Hsu M-C (2021) Computational investigation of left ventricular hemodynamics following bioprosthetic aortic and mitral valve replacement. Mech Res Commun 112:103604

    Google Scholar 

  93. Bazilevs Y, Hsu M-C, Zhang Y, Wang W, Kvamsdal T, Hentschel S, Isaksen J (2010) Computational fluid-structure interaction: methods and application to cerebral aneurysms. Biomech Model Mechanobiol 9:481–498

    Google Scholar 

  94. Arzani A (2018) Accounting for residence-time in blood rheology models: do we really need non-Newtonian blood flow modelling in large arteries? J R Soc Interface 15(146):20180486

    Google Scholar 

  95. Hughes TJR, Wells GN (2005) Conservation properties for the Galerkin and stabilised forms of the advection-diffusion and incompressible Navier-Stokes equations. Comput Methods Appl Mech Eng 194(9):1141–1159

    MathSciNet  MATH  Google Scholar 

  96. Bazilevs Y, Gohean JR, Hughes TJR, Moser RD, Zhang Y (2009) Patient-specific isogeometric fluid-structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device. Comput Methods Appl Mech Eng 198:3534–3550

    MathSciNet  MATH  Google Scholar 

  97. https://www.rhino3d.com/: Rhinoceros3D software

  98. Sacks MS, Zhang W, Wognum S (2016) A novel fibre-ensemble level constitutive model for exogenous cross-linked collagenous tissues. Interface Focus 6:20150090

    Google Scholar 

  99. Zhang W, Zakerzadeh R, Zhang W, Sacks MS (2019) A material modeling approach for the effective response of planar soft tissues for efficient computational simulations. J Mech Behav Biomed Mater 89:168–198

    Google Scholar 

  100. Zhang W, Motiwale S, Hsu M-C, Sacks MS (2021) Simulating the time evolving geometry, mechanical properties, and fibrous structure of bioprosthetic heart valve leaflets under cyclic loading. J Mech Behav Biomed Mater 123:104745

    Google Scholar 

  101. Saad Y, Schultz M (1986) GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput 7:856–869

    MathSciNet  MATH  Google Scholar 

  102. Davis TA (2004) Algorithm 832: UMFPACK v4.3—an unsymmetric-pattern multifrontal method. ACM Trans Math Softw 30(2):196–199

    MathSciNet  MATH  Google Scholar 

  103. Borazjani I (2013) Fluid-structure interaction, immersed boundary-finite element method simulations of bio-prosthetic heart valves. Comput Methods Appl Mech Eng 257:103–116

    MathSciNet  MATH  Google Scholar 

  104. Flamini V, DeAnda A, Griffith BE (2016) Immersed boundary-finite element model of fluid-structure interaction in the aortic root. Theoret Comput Fluid Dyn 30(1):139–164

    Google Scholar 

  105. Becsek B, Pietrasanta L, Obrist D (2020) Turbulent systolic flow downstream of a bioprosthetic aortic valve: velocity spectra, wall shear stresses, and turbulent dissipation rates. Front Physiol 11

  106. Nitti A, De Cillis G, de Tullio MD (2022) Numerical investigation of turbulent features past different mechanical aortic valves. J Fluid Mech 940:43

    MathSciNet  MATH  Google Scholar 

  107. Thubrikar MJ, Deck JD, Aouad J, Nolan SP (1983) Role of mechanical stress in calcification of aortic bioprosthetic valves. J Thorac Cardiovasc Surg 86(1):115–125

    Google Scholar 

  108. https://github.com/david-kamensky/tIGAr: tIGAr source code

  109. Johnson EL, Rajanna MR, Yang C-H, Hsu M-C (2022) Effects of membrane and flexural stiffnesses on aortic valve dynamics: identifying the mechanics of leaflet flutter in thinner biological tissues. Forces Mech 6:100053

    Google Scholar 

Download references

Acknowledgements

G. E. Neighbor and M. Saraeian were partially supported by the Presbyterian Health Foundation Team Science Grant No. C5122401, and M.-C. Hsu was partially supported by the National Heart, Lung, and Blood Institute of the National Institutes of Health under Award No. R01HL142504. H. Zhao was partially supported by National Aeronautics and Space Administration Grant No. 80NSSC21M0070 and D. Kamensky was partially supported by National Science Foundation Grant No. 2103939. This support is gratefully acknowledged. We also thank the Texas Advanced Computing Center (TACC) at the University of Texas at Austin for providing high-performance computing resources that contributed to the results presented in this paper.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Iowa State University, 2043 Black Engineering, Ames, IA, 50011, USA

    Grant E. Neighbor, Mehdi Saraeian & Ming-Chen Hsu

  2. Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, Mail Code 0411, La Jolla, CA, 92093, USA

    Han Zhao & David Kamensky

Authors
  1. Grant E. Neighbor
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Han Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mehdi Saraeian
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ming-Chen Hsu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. David Kamensky
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to David Kamensky.

Ethics declarations

Conflict of interest

The authors have no relevant financial or non-financial interests to disclose.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Neighbor, G.E., Zhao, H., Saraeian, M. et al. Leveraging code generation for transparent immersogeometric fluid–structure interaction analysis on deforming domains. Engineering with Computers 39, 1019–1040 (2023). https://doi.org/10.1007/s00366-022-01754-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-022-01754-y

Keywords

Search

Navigation