A comparison of outlet boundary treatments for prevention of backflow divergence with relevance to blood flow simulations

Computational Mechanics

Volumn 48, Issue 3, 2011, Pages 277-291

  Esmaily Moghadam, Mahdi ^a   Bazilevs, Yuri ^b   Hsia, Tain Yen ^c   Vignon Clementel, Irene E ^d   Marsden, Alison L ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA SAN DIEGO   (United States)

^c GREAT ORMOND STREET HOSPITAL   (United Kingdom)

^d INRIA ROCQUENCOURT   (France)

Author keywords

Cardiovascular simulation; Flow reversal; Lagrange multipliers; Navier Stokes FEM solver; Neumann boundary conditions; Normal velocity constraint; Outflow stabilization; Patient specific blood flow

Indexed keywords

BLOOD; BLOOD VESSELS; BOUNDARY CONDITIONS; HEMODYNAMICS; LAGRANGE MULTIPLIERS; NAVIER STOKES EQUATIONS;

BLOOD FLOW; CARDIOVASCULAR SIMULATIONS; FLOW REVERSALS; NAVIER STOKES; NEUMANN BOUNDARY CONDITION; VELOCITY CONSTRAINTS;

STABILIZATION;

EID: 80052689076     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-011-0599-0     Document Type: Conference Paper

References (42)

1. EL Bove F Migliavacca MR de Leval R Balossino G Pennati TR Lloyd S Khambadkone TY Hsia G Dubini 2008 Use of mathematic modeling to compare and predict hemodynamic effects of the modified blalock-taussig and right ventricle-pulmonary artery shunts for hypoplastic left heart syndrome J Thorac Cardiovasc Surg 136 2 312 320.e2 10.1016/j.jtcvs.2007.04.078
2. F Migliavacca R Balossino G Pennati G Dubini TY Hsia MR de Leval EL Bove 2006 Multiscale modelling in biofluidynamics: application to reconstructive paediatric cardiac surgery J Biomech 39 6 1010 1020 10.1016/j.jbiomech.2005.02. 021
3. K Lagana G Dubini F Migliavacca R Pietrabissa G Pennati A Veneziani A Quarteroni 2002 Multiscale modelling as a tool to prescribe realistic boundary conditions for the study of surgical procedures Biorheology 39 359 364 (Pubitemid 34989030)
4. SA Urquiza PJ Blanco MJ Vnere RA Feijo 2006 Multidimensional modelling for the carotid artery blood flow Comput Meth Appl Mech Eng 195 33-36 4002 4017 1178.76395 10.1016/j.cma.2005.07.014
5. IE Vignon-Clementel CA Figueroa KE Jansen CA Taylor 2006 Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries Comput Meth Appl Mech Eng 195 29-32 3776 3796 2221774 1175.76098 10.1016/j.cma.2005.04.014
6. PJ Blanco RA Feijo SA Urquiza 2007 A unified variational approach for coupling 3d-1d models and its blood flow applications Comput Meth Appl Mech Eng 196 41-44 4391 4410 1173.76430 10.1016/j.cma.2007.05.008 (Pubitemid 47207766)
7. JG Heywood R Rannacher S Turek 1996 Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations Int J Numer Methods Fluids 22 5 325 352 1380844 0863.76016 10.1002/(SICI)1097-0363(19960315) 22:5<325::AID-FLD307>3.0.CO;2-Y (Pubitemid 26472912)
8. L Formaggia JF Gerbeau F Nobile A Quarteroni 2002 Numerical treatment of defective boundary conditions for the Navier-Stokes equations SIAM J Numer Anal 40 376 401 1921924 1020.35070 10.1137/S003614290038296X
9. L Formaggia A Veneziani C Vergara 2008 A new approach to numerical solution of defective boundary valve problems in incompressible fluid dynamics SIAM J Numer Anal 46 6 2769 2794 2439491 05653745 10.1137/060672005
10. CA Taylor TJR Hughes CK Zarins 1998 Finite element modeling of blood flow in arteries Comput Methods Appl Mech Eng 158 1-2 155 196 1626785 0953.76058 10.1016/S0045-7825(98)80008-X (Pubitemid 28424825)
11. CA Taylor CP Cheng LA Espinosa BT Tang D Parker RJ Herfkens 2002 In vivo quantification of blood flow and wall shear stress in the human abdominal aorta during lower limb exercise Ann Biomed Eng 30 402 408 10.1114/1.1476016 (Pubitemid 34690563)
12. K Lagan R Balossino F Migliavacca G Pennati EL Bove MR de Leval G Dubini 2005 Multiscale modeling of the cardiovascular system: application to the study of pulmonary and coronary perfusions in the univentricular circulation J Biomech 38 5 1129 1141 10.1016/j.jbiomech.2004.05.027 (Pubitemid 40431453)
13. AL Marsden IE Vignon-Clementel F Chan JA Feinstein CA Taylor 2007 Effects of exercise and respiration on hemodynamic efficiency in CFD simulations of the total cavopulmonary connection Ann Biomed Eng 35 250 263 10.1007/s10439-006- 9224-3 (Pubitemid 46122180)
14. K Pekkan LP Dasi P Nourparvar S Yerneni K Tobita MA Fogel B Keller A Yoganathan 2008 In vitro hemodynamic investigation of the embryonic aortic arch at late gestation J Biomech 41 8 1697 1706 10.1016/j.jbiomech.2008.03.013
15. K Pekkan O Dur K Sundareswaran K Kanter M Fogel A Yoganathan A Undar 2008 Neonatal aortic arch hemodynamics and perfusion during cardiopulmonary bypass J Biomech Eng 130 6 061012 10.1115/1.2978988
16. TE Tezduyar S Ramakrishnan S Sathe 2008 Stabilized formulations for incompressible flows with thermal coupling Int J Numer Methods Fluids 57 1189 1209 2435089 1140.76024 10.1002/fld.1743
17. TE Tezduyar K Takizawa C Moorman S Wright J Christopher 2010 Space-time finite element computation of complex fluid-structure interactions Int J Numer Methods Fluids 64 1201 1218 05836344 10.1002/fld.2221
18. D de Zelicourt L Ge C Wang F Sotiropoulos A Gilmanov A Yoganathan 2009 Flow simulations in arbitrarily complex cardiovascular anatomies - an unstructured cartesian grid approach Comput Fluids 38 9 1749 1762 1177.76481 10.1016/j.compfluid.2009.03.005
19. AL Marsden JA Feinstein CA Taylor 2008 A computational framework for derivative-free optimization of cardiovascular geometries Comput Methods Appl Mech Eng 197 21-24 1890 1905 2417164 1194.76296 10.1016/j.cma.2007.12.009
20. I Borazjani L Ge F Sotiropoulos 2010 High-resolution fluid-structure interaction simulations of flow through a bi-leaflet mechanical heart valve in an anatomic aorta Ann Biomed Eng 38 326 344 10.1007/s10439-009-9807-x
21. Vignon-Clementel IE (2006) A Coupled Multidomain Method for Computational Modeling of Blood Flow. PhD thesis, Stanford
22. Y Bazilevs JR Gohean TJR Hughes RD Moser Y Zhang 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 45-46 3534 3550 2571821 05634689 10.1016/j.cma.2009. 04.015
23. HJ Kim CA Figueroa TJR Hughes KE Jansen CA Taylor 2009 Augmented lagrangian method for constraining the shape of velocity profiles at outlet boundaries for three-dimensional finite element simulations of blood flow Comput Meth Appl Mech Eng 198 45-46 3551 3566 2571822 05634690 10.1016/j.cma.2009.02. 012
24. AN Brooks TJR Hughes 1982 Streamline upwind/petrov-galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations Comput Methods Appl Mech Eng 32 1-3 199 259 679322 0497.76041 10.1016/0045-7825(82)90071-8
25. TE Tezduyar 2003 Computation of moving boundaries and interfaces and stabilization parameters Int J Numer Methods Fluids 43 5 555 575 2022905 1032.76605 10.1002/fld.505 (Pubitemid 37343253)
26. Y Bazilevs VM Calo JA Cottrell TJR Hughes A Reali G Scovazzi 2007 Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows Comput Methods Appl Mech Eng 197 1-4 173 201 2361475 1169.76352 10.1016/j.cma.2007.07.016 (Pubitemid 47576934)
27. CH Whiting KE Jansen 2001 A stabilized finite element method for the incompressible Navier-Stokes equations using a hierarchical basis Int J Numer Methods Fluids 35 1 93 116 0990.76048 10.1002/1097-0363(20010115)35:1<93:: AID-FLD85>3.0.CO;2-G (Pubitemid 32175047)
28. LP Franca SL Frey 1992 Stabilized finite element methods: II. the incompressible Navier-Stokes equations Comput Methods Appl Mech Eng 99 2-3 209 233 1186727 0765.76048 10.1016/0045-7825(92)90041-H
29. TE Tezduyar S Mittal SE Ray R Shih 1992 Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements Comput Methods Appl Mech Eng 95 221 242 0756.76048 10.1016/0045- 7825(92)90141-6
30. KE Jansen CH Whiting GM Hulbert 2000 A generalized-[alpha] method for integrating the filtered Navier-Stokes equations with a stabilized finite element method Comput Methods Appl Mech Eng 190 3-4 305 319 1808483 0973.76048
31. F Shakib TJR Hughes Z Johan 1989 A multi-element group preconditioned gmres algorithm for nonsymmetric systems arising in finite element analysis Comput Methods Appl Mech Eng 75 1-3 415 456 1035757 0687.76065 10.1016/0045-7825(89)90040-6 (Pubitemid 20640996)
32. Gresho PM, Sani RL (2000) Incompressible flow and the finite element method, vol 2. Wiley
33. Schmidt JP, Delp SL, Sherman MA, Taylor CA, Pande VS, Altman RB (2008) The Simbios National Center: systems biology in motion. In: Proceedings of the IEEE, vol 96, issue 8, pp 1266-1280
34. IE Vignon-Clementel AL Marsden JA Feinstein 2010 A primer on computational simulation in congenital heart disease for the clinician Progress Pediatr Cardiol 30 1-2 3 13 10.1016/j.ppedcard.2010.09.002
35. IE Vignon-Clementel CA Figueroa KE Jansen CA Taylor 2010 Outflow boundary conditions for three-dimensional simulations of non-periodic blood flow and pressure fields in deformable arteries Comput Methods Biomech Biomed Eng 13 5 625 640 10.1080/10255840903413565
36. F Migliavacca G Pennati G Dubini R Fumero R Pietrabissa G Urcelay EL Bove TY Hsia MR De Leval 2001 Modeling of the norwood circulation: effects of shunt size, vascular resistances, and heart rate Am J Physiol Heart Circ Physiol 280 H2076 H2086
37. H Kim IE Vignon-Clementel J Coogan C Figueroa KE Jansen CA Taylor 2010 Patient-specific modeling of blood flow and pressure in human coronary arteries Ann Biomed Eng 38 3195 3209 10.1007/s10439-010-0083-6
38. O Sahni J Muller KE Jansen MS Shephard CA Taylor 2006 Efficient anisotropic adaptive discretization of the cardiovascular system Comput Methods Appl Mech Eng 195 41-43 5634 5655 2243320 1125.76046 10.1016/j.cma.2005.10.018 (Pubitemid 43942195)
39. Y Bazilevs VM Calo Y Zhang TJR Hughes 2006 Isogeometric fluid-structure interaction analysis with applications to arterial blood flow Comput Mech 38 310 322 2246128 1161.74020 10.1007/s00466-006-0084-3 (Pubitemid 43970670)
40. Y Bazilevs VM Calo TJR Hughes Y Zhang 2008 Isogeometric fluid-structure interaction: theory, algorithms, and computations Comput Mech 43 3 37 2443159 1169.74015 10.1007/s00466-008-0315-x
41. K Takizawa C Moorman S Wright J Purdue T McPhail PR Chen J Warren TE Tezduyar 2011 Patient-specific arterial fluid-structure interaction modeling of cerebral aneurysms Int J Numer Methods Fluids 65 308 323 1203.92044 10.1002/fld.2360
42. Tezduyar TE, Takizawa K, Brummer T, Chen PR (2011) Space-time fluid-structure interaction modeling of patient-specific cerebral aneurysms. Int J Numer Methods Biomed Eng 27. doi: 10.1002/cnm.1433