Immersed boundary method and lattice Boltzmann method coupled FSI simulation of mitral leaflet flow

Computers and Fluids

Volumn 39, Issue 5, 2010, Pages 871-881

  Cheng, Yongguang ^a   Zhang, Hui ^a  

^a WUHAN UNIVERSITY   (China)

Author keywords

Coupling; Fluid structure interaction; Immersed boundary method; Lattice Boltzmann method; Mitral leaflet flow

Indexed keywords

BOUNDARY MOTION; COUPLED SIMULATION; COUPLING FLUIDS; COUPLING METHODS; COUPLING SCHEME; FLEXIBLE BOUNDARIES; FLOW DYNAMICS; HEART MODEL; IMMERSED BOUNDARY; IMMERSED BOUNDARY METHODS; JET FLOW; LATTICE BOLTZMANN METHOD; MEASURED DATA; MITRAL VALVES; MOVING BOUNDARIES; SECOND-ORDER ACCURACY; VENTRICULAR PRESSURE;

COMPUTATIONAL FLUID DYNAMICS; DROP FORMATION; FLEXIBLE STRUCTURES; FLOW PATTERNS; FLUID STRUCTURE INTERACTION; FLUIDS; HEART; JETS; PRESSURE GRADIENT; THREE DIMENSIONAL;

TURBULENT FLOW;

EID: 76949105767     PISSN: 00457930     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compfluid.2010.01.003     Document Type: Article

References (46)

1. Peskin CS. Flow patterns around heart valves: a digital computer method for solving the equations of motion, vol. 378. PhD thesis, Albert Einstein College of Medicine; Univ. Microfilms; 1972. p. 72-102.
2. Peskin C.S., and McQueen D.M. In: Ellington C.P., et al. (Ed). A general method for the computer simulation of biological systems interacting with fluids-biological fluid dynamics (1995), The Company of Biologists Limited, Cambridge
3. McQueen D.M., and Peskin C.S. A three-dimensional computer model of the human heart for studying cardiac fluid dynamics. Comp Graph 34 (2000) 56-60
4. Lemmon J.D., and Yoganathan A.P. Three-dimensional computational model of left heart diastolic function with fluid-structure interaction. J Biomech Eng 122 (2000) 109-117
5. Lemmon J.D., and Yoganathan A.P. Computational modeling of left heart diastolic function: examination of ventricular dysfunction. J Biomech Eng 122 (2000) 297-303
6. Miller L.A., and Peskin C.S. When vortices stick: an aerodynamic transition in tiny insect flight. J Exp Biol 207 (2004) 3073-3088
7. Mitta R, Dong H, Bozkurttas M, Loebbecke A. Analysis of flying and swimming in nature using an immersed boundary method. In: 36th AIAA fluid dynamics conference and exhibit, San Francisco, California; 2006.
8. Fauci L.J., and Peskin C.S. A computational model of aquatic animal locomotion. J Comp Phys 77 (1988) 85-108
9. Zhu L.D., and Peskin C.S. Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method. J Comp Phys 179 (2002) 452-468
10. Zhu LD. An immersed boundary method by the lattice Boltzmann approach in three dimensions. In: The sixth international conference on mesoscopic methods in engineering and science, Guangzhou, China; July 2009.
11. Zhang J., Johnson P.C., and Popel A.S. An immersed boundary lattice Boltzmann approach to simulate deformable liquid capsules and its application to microscopic blood flows. Phys Biol 4 (2007) 285-295
12. Zhang J., Johnson P.C., and Popel A.S. Red blood cell aggregation and dissociation in shear flows simulated by lattice Boltzmann method. J Biomech 41 (2008) 47-55
13. Dillon R., Fauei L.J., Fogelson A.L., and Gaver D. Modeling biofilm processes using the immersed boundary method. J Comp Phys 129 (1996) 57-73
14. Kim Y., and Peskin C.S. 2-D parachute simulation by the immersed boundary method. SIAM J Sci Comp 28 (2006) 2294-2312
15. Kim Y., and Peskin C.S. 3-D parachute simulation by the immersed boundary method. Comp Fluids 38 (2009) 1080-1090
16. Peskin C.S. The immersed boundary method. Acta Numer 11 (2002) 479-517
17. Chen S., and Doolen G.D. Lattice Boltzmann method for fluid flows. Annu Rev Fluid Mech 30 (1998) 329-364
18. Zheng H.W., Shu C., and Chew Y.T. A lattice Boltzmann model for multiphase flows with large density ratio. J Comp Phys 218 (2006) 353-371
19. Pan C.X., Luo L.S., and Miller C.T. An evaluation of lattice Boltzmann schemes for porous medium flow simulation. Comp Fluids 35 (2006) 898-909
20. Chen S., Chen H.D., Martinez D., and Matthaeus W. Lattice Boltzmann model for simulation of magnetohydrodynamics. Phys Rev Lett 67 (1991) 3776-3779
21. Aidun C.K., and Lu Y.N. Lattice Boltzmann simulation of solid particles suspended in fluid. J Stat Phys 81 (1995) 49-61
22. Zhang R., Shan X., and Chen H. Efficient kinetic method for fluid simulation beyond the Navier-Stokes equation. Phys Rev E 74 (2006) 046703
23. Gan Y.B., Xu A.G., Zhang G.C., Yu X.J., and Li Y. Two-dimensional lattice Boltzmann model for compressible flows with high Mach number. Physica A 387 (2008) 1721-1732
24. Feng Z.G., and Michaelides E.E. The immersed boundary-lattice Boltzmann method for solving fluid-particles interaction problems. J Comp Phys 195 (2004) 602-628
25. Peng Y., Shu C., et al. Application of multi-block approach in the immersed boundary-lattice Boltzmann method for viscous fluid flows. J Comp Phys 218 (2006) 460-478
26. Shu C., Liu N., and Chew Y.T. A novel immersed boundary velocity correction-lattice Boltzmann method and its application to simulate flow past a circular cylinder. J Comp Phys 226 (2007) 1607-1622
27. Dupuis A., Chatelain P., and Koumoutsakos P. An immersed boundary-lattice Boltzmann method for the simulation of the flow past an impulsively started cylinder. J Comp Phys 227 (2008) 4486-4498
28. Niu X.D., Shu C., Chew Y.T., and Peng Y. A momentum exchange-based immersed boundary-lattice Boltzmann method for simulating incompressible viscous flows. Phys Lett A 354 (2006) 173-182
29. Cheng Y.G., and Li J.P. Introducing unsteady non-uniform source terms into the lattice Boltzmann model. Int J Num Meth Fluids 56 (2008) 629-641
30. Peskin C.S., and Printz B.F. Improved volume conservation in the computation of flows with immersed elastic boundaries. J Comp Phys 105 (1993) 33-46
31. Lee L., and LeVeque R.J. An immersed interface method for incompressible Navier-Stokes equations. SIAM J Sci Comp 25 (2003) 832-856
32. Xu S., and Wang Z.J. An immersed interface method for simulating the interaction of a fluid with moving boundaries. J Comp Phys (2006) 216;454-493
33. Oertel H. Prandtl's essentials of fluid mechanics (2004), Springer Press, New York
34. Courtois M., Kovacs S.J., and Ludbrook P.A. Transmitral pressure-flow velocity relation: importance of regional pressure gradients in the left ventricle during diastole. Circulation 78 (1988) 661-671
35. Ebbers T., Wigstroem L., Bolger A.F., Wranne B., and Karlsson M. Noninvasive measurement of time-varying three-dimensional relative pressure fields within the human heart. J Biomech Eng 124 (2002) 288-293
36. Saber N.R., Wood N.B., Gosman A.D., Merrifield R.D., Yang G.Z., Charrier C.L., et al. Progress towards patient-specific computational flow modeling of the left heart via combination of magnetic resonance imaging with computational fluid dynamics. Ann Biomed Eng 31 1 (2003) 42-52
37. Nakamura M., Wada S., Mikami T., Kitabatake A., and Karino T. Computational study on the evolution of an intraventricular vortical flow during early diastole for the interpretation of color M-mode Doppler echocardiograms. Biomech Model Mechanobiol 2 (2003) 59-72
38. Jacob M.J., Pernille T.A., et al. Evaluation of a 2D model of the left side of the human heart against magnetic resonance velocity mapping. Cardiovasc Eng 1 2 (2001) 59-76
39. McQueen D.M., Peskin C.S., and Yellin E.L. Fluid dynamics of the mitral valve physiological aspects of a mathematical model. Am J Physiol 242 (1982) H1095-H1110
40. Watton P., Luo X., Wang X., Bernacca G., Molloy P., and Wheatley D. Dynamic modelling of prosthetic chorded mitral valves using the immersed boundary method. J Biomech 40 3 (2007) 613-626
41. d'Humires D., Ginzburg I., Krafczyk M., Lallemand P., and Luo L.S. Multiple-relaxation-time lattice Boltzmann models in three dimensions. Philos Trans Roy Soc A 360 (2002) 437-451
42. Newren EP. Enhancing the immersed boundary method: stability, volume conservation and implicit solvers. PhD dissertation of the University of Utah, USA; 2007.
43. Mittal R., and Iaccarino G. Immersed boundary methods. Annu Rev Fluid Mech 37 (2003) 226-239
44. Griffith B.E., and Peskin C.S. On the order of accuracy of the immersed boundary method: higher order convergence rates for sufficiently smooth problems. J Comp Phys 208 (2005) 75-105
45. Le G., and Zhang J. Boundary slip from the immersed boundary lattice Boltzmann models. Phys Rev E 79 2 (2009) 026701
46. Lallemand P., and Luo L.S. Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability. Phys Rev E 61 6 (2000) 6546-6562