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Simulation of high-Reynolds number vascular flows. (English) Zbl 1120.76076

Summary: We describe a spectral element solution strategy for simulation of weakly turbulent vascular flows. Novel approaches are presented for treatment of outflow boundary conditions and flow division. We demonstrate that several million gridpoints are required to obtain converged rms statistics when uniform refinement is used, and discuss possible approaches to cost reduction.

MSC:

76Z05 Physiological flows
76M22 Spectral methods applied to problems in fluid mechanics
92C35 Physiological flow
65Y05 Parallel numerical computation
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[1] N. Arslan, Experimental characterization of transitional unsteady flow inside a graft-to-vein junction, Ph.D. thesis, University of Illinois, Chicago, 1999, Department of Mechanical Engineering.; N. Arslan, Experimental characterization of transitional unsteady flow inside a graft-to-vein junction, Ph.D. thesis, University of Illinois, Chicago, 1999, Department of Mechanical Engineering.
[2] Caro, C. G.; Fitz-Gerald, J. M.; Schroter, R. C., Arterial wall shear and distribution of early atheroma in man, Nature, 223, 211, 1159-1160 (1969)
[3] W. Couzy, Spectral element discretization of the unsteady Navier-Stokes equations and its iterative solution on parallel computers, Ph.D. thesis, Swiss Federal Institute of Technology-Lausanne, 1995, Thesis no. 1380.; W. Couzy, Spectral element discretization of the unsteady Navier-Stokes equations and its iterative solution on parallel computers, Ph.D. thesis, Swiss Federal Institute of Technology-Lausanne, 1995, Thesis no. 1380.
[4] Davies, M. J.; Woolf, N.; Rowles, P. M.; Pepper, J., Morphology of the endothelium over atherosclerotic plaques in human coronary arteries, Br. Heart J., 60, 6, 459-464 (1988)
[5] DePaola, N.; Gimbrone, M. A.; Davies, P. F.; Dewey, C. F., Vascular endothelium responds to fluid shear stress gradients, Arterioscler. Thromb., 12, 11, 1254-1257 (1992)
[6] Deville, M. O.; Fischer, P. F.; Mund, E. H., High-order methods for incompressible fluid flow (2002), Cambridge University Press: Cambridge University Press Cambridge · Zbl 1007.76001
[7] Ethier, C. R.; Prakash, S.; Steinman, D. A.; Leask, R. L.; Couch, G. G.; Ojha, M., Steady flow separation patterns in a 45 degree junction, J. Fluid Mech., 411, 1-38 (2000) · Zbl 0949.76504
[8] Fillinger, M. F.; Reinitz, E. R.; Schwartz, R. A.; Resetarits, D. E.; Paskanik, A. M.; Bredenberg, C. E., Beneficial effects of banding on venous intimal-medial hyperplasia in arteriovenous loop grafts, J. Vasc. Surg., 11, 4, 556-566 (1990)
[9] Fischer, P. F., An overlapping Schwarz method for spectral element solution of the incompressible Navier-Stokes equations, J. Comput. Phys., 133, 84-101 (1997) · Zbl 0904.76057
[10] Fischer, P. F.; Kruse, G. W.; Loth, F., Spectral element methods for transitional flows in complex geometries, J. Sci. Comput., 17, 81-98 (2002) · Zbl 1001.76075
[11] Fischer, P. F.; Lottes, J. W., Hybrid Schwarz-multigrid methods for the spectral element method: Extensions to Navier-Stokes, (Kornhuber, R.; Hoppe, R.; Périaux, J.; Pironneau, O.; Widlund, O.; Xu, J., Domain Decomposition Methods in Science and Engineering Series (2004), Springer: Springer Berlin) · Zbl 1067.65123
[12] Fischer, P. F.; Miller, N. I.; Tufo, H. M., An overlapping Schwarz method for spectral element simulation of three-dimensional incompressible flows, (Bjørstad, P.; Luskin, M., Parallel Solution of Partial Differential Equations (2000), Springer: Springer Berlin), 158-180 · Zbl 0991.76059
[13] Fischer, P. F.; Mullen, J. S., Filter-based stabilization of spectral element methods, Comptes rendus de l’Académie des sciences, Sér. I - Anal. Numér., 332, 265-270 (2001)
[14] Fry, D. L., Acute vascular endothelial changes associated with increased blood velocity gradients, Circ. Res., 22, 2, 165-197 (1968)
[15] Gertz, S. D.; Roberts, W. C., Hemodynamic shear force in rupture of coronary arterial atherosclerotic plaques, Am. J. Cardiol., 66, 19, 1368-1372 (1990)
[16] Gin, R.; Straatman, A. G.; Steinman, D. A., A dual-pressure boundary condition for use in simulations of bifurcating conduits, J. Biomech. Engrg., 124, 617-619 (2002)
[17] Glagov, S.; Zarins, C. K.; Giddens, D. P.; Ku, D. N., Hemodynamics and atherosclerosis. insights and perspectives gained from studies of human arteries, Arch. Pathol. Lab. Med., 112, 1018-1031 (1988)
[18] Gordon, W. J.; Hall, C. A., Transfinite element methods: blending-function interpolation over arbitrary curved element domains, Numer. Math., 21, 109-129 (1973) · Zbl 0254.65072
[19] Gottlieb, D.; Orszag, S. A., Numerical analysis of spectral methods: Theory and applications (1977), SIAM-CBMS: SIAM-CBMS Philadelphia · Zbl 0412.65058
[20] Hellums, J. D., The resistance to oxygen transport in the capillaries relative to that in the surrounding tissue, Microvasc. Res., 13, 1, 131-136 (1977)
[21] L.W. Ho, A Legendre spectral element method for simulation of incompressible unsteady viscous free-surface flows, Ph.D. thesis, Massachusetts Institute of Technology, 1989, Cambridge, MA, USA.; L.W. Ho, A Legendre spectral element method for simulation of incompressible unsteady viscous free-surface flows, Ph.D. thesis, Massachusetts Institute of Technology, 1989, Cambridge, MA, USA.
[22] Hsu, L. C.; Mavriplis, C., Adaptive meshes for the spectral element method, (Bjørstad, P.; Espedal, M.; Keyes, D., Domain Decomposition 9th Proc. (1997), John-Wiley: John-Wiley New York), 374-381
[23] Hutchison, K. J.; Karpinski, E., In vivo demonstration of flow recirculation and turbulence downstream stenoses in canine arteries, J. Biomech., 18, 285-296 (1985)
[24] Jeong, J.; Hussain, F., On the identification of a vortex, J. Fluid Mech., 285, 69-94 (1995) · Zbl 0847.76007
[25] Klebanoff, P. S.; Cleveland, W. G.; Tidstrom, K. D., On the evolution of a turbulent boundary layer induced by a three-dimensional roughness element, J. Fluid Mech., 92, 101-187 (1992)
[26] Ku, D. N., Blood flow in arteries, Annu. Rev. Fluid Mech., 29, 399-434 (1997)
[27] Ku, D. N.; Giddens, D. P.; Zarins, C. K.; Glagov, S., Pulsatile flow and atherosclerosis in the human carotid bifurcation, Arteriosclerosis, 5, 3, 293-302 (1985)
[28] S.E. Lee, Solution method for transitional flow in a vascular bifurcation based on in vivo medical images, Master’s thesis, Univ. of Illinois, Chicago, 2002, Department of Mechanical Engineering.; S.E. Lee, Solution method for transitional flow in a vascular bifurcation based on in vivo medical images, Master’s thesis, Univ. of Illinois, Chicago, 2002, Department of Mechanical Engineering.
[29] S.E. Lee, S.W. Lee, P.F. Fischer, H.S. Bassiouny, F. Loth, Direct numerical simulation of transitional flow in a stenosed carotid bifurcation, J. Biomech., submitted for publication.; S.E. Lee, S.W. Lee, P.F. Fischer, H.S. Bassiouny, F. Loth, Direct numerical simulation of transitional flow in a stenosed carotid bifurcation, J. Biomech., submitted for publication.
[30] Lee, S. W.; Fischer, P. F.; Loth, F.; Royston, T. J.; Grogan, J. K.; Bassiouny, H. S., Flow-induced vein-wall vibration in an arteriovenous graft, J. Fluids Struct., 20, 837-852 (2005)
[31] S.W. Lee, D.S. Smith, F. Loth, P.F. Fischer, H.S. Bassiouny, Importance of flow division on transition to turbulence within an arteriovenous graft, J. Biomech., in press.; S.W. Lee, D.S. Smith, F. Loth, P.F. Fischer, H.S. Bassiouny, Importance of flow division on transition to turbulence within an arteriovenous graft, J. Biomech., in press.
[32] Lee, S. W.; Smith, D. S.; Loth, F.; Fischer, P. F.; Bassiouny, H. S., Numerical and experimental simulation of transitional flow in a blood vessel junction, Numer. Heat Transfer, 51, 1-22 (2007)
[33] Loth, F.; Arslan, N.; Fischer, P. F.; Bertram, C. D.; Lee, S. E.; Royston, T. J.; Song, R. H.; Shaalan, W. E.; Bassiouny, H. S., Transitional flow at the venous anastomosis of an arteriovenous graft: Potential relationship with activation of the ERK1/2 mechanotransduction pathway, ASME J. Biomech. Engrg., 125, 49-61 (2003)
[34] Lottes, J. W.; Fischer, P. F., Hybrid multigrid/Schwarz algorithms for the spectral element method, J. Sci. Comput., 24, 45-78 (2005) · Zbl 1078.65570
[35] Maday, Y.; Patera, A. T., Spectral element methods for the Navier-Stokes equations, (Noor, A. K.; Oden, J. T., State-of-the-Art Surveys in Computational Mechanics (1989), ASME: ASME New York), 71-143
[36] Maday, Y.; Patera, A. T.; Rønquist, E. M., An operator-integration-factor splitting method for time-dependent problems: Application to incompressible fluid flow, J. Sci. Comput., 5, 263-292 (1990) · Zbl 0724.76070
[37] Mavriplis, C., Adaptive mesh strategies for the spectral element method, Comput. Methods Appl. Mech. Engrg., 116, 77-86 (1994) · Zbl 0826.76070
[38] Murray, C. J.; Lopez, A. D., Alternative projections of mortality and disability by cause 1990-2020: Global burden of disease study, Lancet, 349, 9064, 1498-1504 (1997)
[39] Orszag, S. A., Spectral methods for problems in complex geometry, J. Comput. Phys., 37, 70-92 (1980) · Zbl 0476.65078
[40] Perot, J. B., An analysis of the fractional step method, J. Comput. Phys., 108, 51-58 (1993) · Zbl 0778.76064
[41] Ram, S. J.; Magnasco, A.; Jones, S. A.; Barz, A.; Zsom, L.; Swamy, S.; Paulson, W. D., In vivo validation of glucose pump test for measurement of hemodialysis access flow, Am. J. Kidney Dis., 42, 4, 752-760 (2003)
[42] Ramstack, J. M.; Zuckerman, L.; Mockros, L. F., Shear-induced activation of platelets, J. Biomech., 12, 2, 113-125 (1979)
[43] Sherwin, S. J.; Blackburn, H. M., Three-dimensional instabilities and transition of steady and pulsatile axisymmetric stenotic flows, J. Fluid Mech., 533, 297-327 (2005) · Zbl 1074.76021
[44] C.S. Verma, P.F. Fischer, S.E. Lee, F. Loth, An all-hex meshing strategy for bifurcation geometries in vascular flow simulation, in: Proc. of the 14th Int. Meshing Roundtable Conf., San Diego, 2005.; C.S. Verma, P.F. Fischer, S.E. Lee, F. Loth, An all-hex meshing strategy for bifurcation geometries in vascular flow simulation, in: Proc. of the 14th Int. Meshing Roundtable Conf., San Diego, 2005.
[45] White, C. R.; Haidekker, M.; Bao, X.; Frangos, J. A., Temporal gradients in shear, but not spatial gradients, stimulate endothelial cell proliferation, Circulation, 103, 20, 2508-2513 (2001)
[46] Zarins, C. K.; Giddens, D. P.; Bharadvaj, B. K.; Sottiurai, V. S.; Mabon, R. F.; Glagov, S., Carotid bifurcation atherosclerosis. quantitative correlation of plaque localization with flow velocity profiles and wall shear stress, Circ. Res., 53, 4, 502-514 (1983)
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