Skip to main content
Log in

Cardiovascular flow simulation at extreme scale

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

As cardiovascular models grow more sophisticated in terms of the geometry considered, and more physiologically realistic boundary conditions are applied, and fluid flow is coupled to structural models, the computational complexity grows. Massively parallel adaptivity and flow solvers with extreme scalability enable cardiovascular simulations to reach an extreme scale while keeping the time-to-solution reasonable. In this paper, we discuss our efforts in this area and provide two demonstrations: one on an extremely large and complex geometry (including many of the major arteries below the neck) where the solution is efficiently captured with anisotropic adaptivity and another case (severe abdominal aorta aneurysm) where the transitional flow leads to extremely large meshes (O(109)) and scalability to extremely large core counts (O(105)) for both rigid and deforming wall simulations.

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.

Similar content being viewed by others

References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. Bazilevs Y, Hsu M-C, Benson DJ, Sankaran S, Marsden AL (2009) Computational fluidstructure interaction: methods and application to a total cavopulmonary connection. Comput Mech (submitted)

  3. Boman E, Devine K, Fisk LA, Heaphy R, Hendrickson B, Leung V, Vaughan C, Catalyurek U, Bozdag D, Mitchell W (1999) Zoltan home page. http://www.cs.sandia.gov/Zoltan

  4. Brooks AN, Hughes TJR (1982) Streamline upwind/petrov-galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. Comp Methods Appl Mech Eng 32: 199–259

    Article  MathSciNet  MATH  Google Scholar 

  5. Cebral JR, Castro MA, Burgess JE, Pergolizzi RS, Sheridan MJ, Putman CM (2005) Characterization of cerebral aneurysms for assessing risk of rupture by using patient-specific computational hemodynamics models. AJNR Am J Neuroradiol 26(10): 2550–2559

    Google Scholar 

  6. Farhat C, Geuzaine P (2004) Design and analysis of robust ale time-integrators for the solution of unsteady flow problems on moving grids. Comp Methods Appl Mech Eng 193: 4073–4095

    Article  MathSciNet  MATH  Google Scholar 

  7. Fernandez MA, Le Tallec P (2003) Linear stability analysis in fluid–structure interaction with transpiration. Part ii: numerical analysis and applications. Comp Methods Appl Mech Eng 192: 4837–4873

    Article  MathSciNet  MATH  Google Scholar 

  8. Figueroa CA, Vignon-Clementel IE, Jansen KE, Hughes TJR, Taylor CA (2006) A coupled momentum method for modeling blood flow in three-dimensional deformable arteries. Comp Methods Appl Mech Eng 195(41–43): 5685–5706

    Article  MathSciNet  MATH  Google Scholar 

  9. Formaggia L, Gerbeau JF, Nobile F, Quarteroni A (2002) Numerical treatment of defective boundary conditions for the Navier–Stokes equations. SIAM J Numer Anal 40(1): 376–401

    Article  MathSciNet  MATH  Google Scholar 

  10. Franca LP, Frey SL (1992) Stabilized finite element methods ii. the incompressible Navier–Stokes equations. Comp Methods Appl Mech Eng 99(2–3): 209–233

    Article  MathSciNet  MATH  Google Scholar 

  11. Jansen KE, Whiting CH, Hulbert GM (2000) Generalized-α method for integrating the filtered Navier–Stokes equations with a stabilized finite element method. Comp Methods Appl Mech Eng 190(3–4): 305–319

    MathSciNet  MATH  Google Scholar 

  12. Karypis G, Kumar V (1999) Parallel multilevel k-way partitioning scheme for irr. graphs. SIAM Rev 41: 278–300

    Article  MathSciNet  MATH  Google Scholar 

  13. LaDisa JF, Olson LE, Molthen RC, Hettrick DA, Pratt PF, Hardel MD, Kersten JR, Warltier DC, Pagel PS (2005) Alterations in wall shear stress predict sites of neointimal hyperplasia after stent implantation in rabbit iliac arteries. Am J Phys Heart Circ Phys 288: H2465–H2475

    Article  Google Scholar 

  14. Laskey WK, Parker HG, Ferrari VA, Kussmaul WG, Noordergraaf A (1990) Estimation of total systemic arterial compliance in humans. J Appl Physiol 69(1): 112–119

    Google Scholar 

  15. Les AS, Shadden SC, Figueroa CA, Park JM, Tedesco MM, Herfkens RJ, Taylor CA, Dalman RL (2009) Quantification of hemodynamics in abdominal aortic aneurysms during rest and exercise using magnetic resonance imaging and computational fluid dynamic. Ann Biomed Eng (submitted)

  16. Li Z, Kleinstreuer C (2005) Blood flow and structure interactions in a stented abdominal aortic aneurysm model. Med Eng Phys 27(5): 369–382

    Article  Google Scholar 

  17. Migliavacca F, Balossino R, Pennati G, Dubini G, Hsia TY, de Leval MR, Bove EL (2006) Multiscale modelling in biofluidynamics: application to reconstructive paediatric cardiac surgery. J Biomech 39(6): 1010–1020

    Article  Google Scholar 

  18. Perktold K, Peter R, Resch M (1989) Pulsatile non-newtonian blood flow simulation through a bifurcation with an aneurysm. Biorheology 26(6): 1011–1030

    Google Scholar 

  19. Peskin CS, McQueen DM (1995) A general method for the computer simulation of biological systems interacting with fluids. Symp Soc Exp Biol 49: 265–276

    Google Scholar 

  20. Quarteroni A, Ragni S, Veneziani A (2001) Coupling between lumped and distributed models for blood flow problems. Comp Vis Sci 4(2): 111–124

    Article  MathSciNet  MATH  Google Scholar 

  21. Quarteroni A, Tuveri M, Veneziani A (2000) Computational vascular fluid dynamics: problems, models and methods. Comp Vis Sci 2(4): 163–197

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  23. Sahni O, Müller Y, Jansen KE, Shephard MS, Taylor CA (2006) Efficient anisotropic adaptive discretization of the cardiovascular system. Comp Methods Appl Mech Eng 195: 5634–5655

    Article  MATH  Google Scholar 

  24. 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 IEEE/ACM SC’09, Finalist paper for the Gordon Bell Prize

  25. Shephard MS, Jansen KE, Sahni O, Diachin LA (2007) Parallel adaptive simulations on unstructured meshes. J Phys Conf Ser 78. doi:10.1088/1742-6596/78/1/012053

  26. Soerensen DD, Pekkan K, de Zelicourt D, Sharma S, Kanter K, Fogel M, Yoganathan AP (2007) Introduction of a new optimized total cavopulmonary connection. Ann Thorac Surg 83(6): 2182–2190

    Article  Google Scholar 

  27. Stergiopulos N, Segers P, Westerhof N (1999) Use of pulse pressure method for estimating total arterial compliance in vivo. Am J Physiol Heart Circ Physiol 276(2): H424–H428

    Google Scholar 

  28. Stuhne GR, Steinman DA (2004) Finite-element modeling of the hemodynamics of stented aneurysms. J Biomech Eng 126(3): 382–387

    Article  Google Scholar 

  29. Tang BT, Cheng CP, Draney MT, Wilson NM, Tsao PS, Herfkens RJ, Taylor CA (2006) Abdominal aortic hemodynamics in young healthy adults at rest and during lower limb exercise: quantification using image-based computer modeling. Am J Physiol Heart Circ Physiol 291(2): H668–H676

    Article  Google Scholar 

  30. Taylor CA, Hughes TJR, Zarins CK (1998) Finite element modeling of blood flow in arteries. Comput Methods Appl Mech Eng 158(1–2): 155–196

    Article  MathSciNet  MATH  Google Scholar 

  31. Taylor CA, Draney MT (2004) Experimental and computational methods in cardiovascular fluid mechanics. Annu Rev Fluid Mech 36: 197–231

    Article  MathSciNet  Google Scholar 

  32. Taylor CA, Draney MT, Ku JP, Parker D, Steele BN, Wang K, Zarins CK (1999) Predictive medicine: computational techniques in therapeutic decision-making. Comp Aided Surg 4(5): 231–247

    Article  Google Scholar 

  33. Tezduyar TE, Behr M, Liou J (1992) A new strategy for finite element computations involving moving boundaries and interfaces -the deforming-spatial-domain/space–time procedure: I. the concept and the preliminary numerical tests. Comput Methods Appl Mech Eng 94: 339–351

    Article  MathSciNet  MATH  Google Scholar 

  34. Vignon-Clementel IE, Figueroa CA, Jansen KE, Taylor CA (2008) Outflow boundary conditions for three-dimensional simulations of non-periodic blood flow and pressure fields in deformable arteries. Comput Meth Biomech Biomed Eng (submitted)

  35. Vignon-Clementel IE, Figueroa CA, Jansen KE, Taylor CA (2006) Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries. Comp Methods Appl Mech Eng 195(29–32): 3776–3796

    Article  MathSciNet  MATH  Google Scholar 

  36. Whiting CH, Jansen KE (2001) A stabilized finite element method for the incompressible Navier–Stokes equations using a hierarchical basis. Int J Numer Meth Fluids 35: 93–116

    Article  MATH  Google Scholar 

  37. Womersley J (1955) Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. J Physiol 127: 553–563

    Google Scholar 

  38. Zamir M, Sinclair P, Wonnacott TH (1992) Relation between diameter and flow in major branches of the arch of the aorta. J Biomech 25(11): 1303–1310

    Article  Google Scholar 

  39. Zhou M (2009) Petascale adaptive computational fluid dynamics. Ph.D. thesis, Rensselaer Polytechnic Institute

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kenneth E. Jansen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhou, M., Sahni, O., Kim, H.J. et al. Cardiovascular flow simulation at extreme scale. Comput Mech 46, 71–82 (2010). https://doi.org/10.1007/s00466-009-0450-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-009-0450-z

Keywords

Navigation