Geodesic
Simulation of the Three-Dimensional Flow of Blood Using a Shear-Thinning Viscoelastic Fluid Model
T. Bodnár1 ; K.R. Rajagopal2 ; A. Sequeira3
1 Department of Technical Mathematics, Faculty of Mechanical Engineering Czech Technical University, Náměstí 13, 121 35 Prague 2, Czech Republic
2 Department of Mechanical Engineering, Texas A & M University College Station, TX 77843-3123, USA
3 Department of Mathematics and CEMAT/IST, Instituto Superior Técnico Technical University of Lisbon, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal
Mathematical modelling of natural phenomena, Tome 6 (2011) no. 5, pp. 1-24

Voir la notice de l'article provenant de la source EDP Sciences

This paper is concerned with the numerical simulation of a thermodynamically compatible viscoelastic shear-thinning fluid model, particularly well suited to describe the rheological response of blood, under physiological conditions. Numerical simulations are performed in two idealized three-dimensional geometries, a stenosis and a curved vessel, to investigate the combined effects of flow inertia, viscosity and viscoelasticity in these geometries. The aim of this work is to provide new insights into the modeling and simulation of homogeneous rheological models for blood and a basis for further developments in modeling and prediction.
DOI : 10.1051/mmnp/20116501

T. Bodnár 1 ; K.R. Rajagopal 2 ; A. Sequeira 3

1 Department of Technical Mathematics, Faculty of Mechanical Engineering Czech Technical University, Náměstí 13, 121 35 Prague 2, Czech Republic
2 Department of Mechanical Engineering, Texas A & M University College Station, TX 77843-3123, USA
3 Department of Mathematics and CEMAT/IST, Instituto Superior Técnico Technical University of Lisbon, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal 
@article{10_1051_mmnp_20116501,
     author = {T. Bodn\'ar and K.R. Rajagopal and A. Sequeira},
     title = {Simulation of the {Three-Dimensional} {Flow} of {Blood} {Using} a {Shear-Thinning} {Viscoelastic} {Fluid} {Model}},
     journal = {Mathematical modelling of natural phenomena},
     pages = {1--24},
     publisher = {mathdoc},
     volume = {6},
     number = {5},
     year = {2011},
     doi = {10.1051/mmnp/20116501},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20116501/}
}
TY  - JOUR
AU  - T. Bodnár
AU  - K.R. Rajagopal
AU  - A. Sequeira
TI  - Simulation of the Three-Dimensional Flow of Blood Using a Shear-Thinning Viscoelastic Fluid Model
JO  - Mathematical modelling of natural phenomena
PY  - 2011
SP  - 1
EP  - 24
VL  - 6
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20116501/
DO  - 10.1051/mmnp/20116501
LA  - en
ID  - 10_1051_mmnp_20116501
ER  - 
%0 Journal Article
%A T. Bodnár
%A K.R. Rajagopal
%A A. Sequeira
%T Simulation of the Three-Dimensional Flow of Blood Using a Shear-Thinning Viscoelastic Fluid Model
%J Mathematical modelling of natural phenomena
%D 2011
%P 1-24
%V 6
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20116501/
%R 10.1051/mmnp/20116501
%G en
%F 10_1051_mmnp_20116501
T. Bodnár; K.R. Rajagopal; A. Sequeira. Simulation of the Three-Dimensional Flow of Blood Using a Shear-Thinning Viscoelastic Fluid Model. Mathematical modelling of natural phenomena, Tome 6 (2011) no. 5, pp. 1-24. doi: 10.1051/mmnp/20116501

[1] M. Anand, K.R. Rajagopal Int. J. of Cardiovascular Medicine and Science 2004 59 68

[2] M. Anand, K.R. Rajagopal C. R. Méchanique 2002 557 562

[3] M. Anand, K. Rajagopal, K.R. Rajagopal J. of Theoretical Medicine 2003 183 218

[4] M. Anand, K. Rajagopal, K.R. Rajagopal Pathophysiology Haemostasis Thrombosis 2005 109 120

[5] M. Anand, K. Rajagopal, K.R. Rajagopal J. of Theoretical Biology 2008 725 738

[6] N. Arada, M. Pires, A. Sequeira. Viscosity effects on flows of generalized Newtonian fluids through curved pipes. Computers and Mathematics with Applications, 53 (2007), pp. 625-646.

[7] N. Arada, M. Pires, A. Sequeira. Numerical simulations of shear-thinning Oldroyd-B fluids in curved pipes. IASME Transactions, Issue 6, 2 (2005), pp. 948-959.

[8] P.D. Bailyk, D.A. Steinman, C.R. Ethier Biorheology 1994 565 586

[9] A.A. Berger, L. Talbot, L.-S. Yao Annu. Rev. Fluid Mech. 1983

[10] T. Bodnár, A. Sequeira. Numerical Study of the Significance of the Non-Newtonian Nature of Blood in Steady Flow Through a Stenosed Vessel. In: Advances in Mathematical Fluid Mechanics (edited by R. Rannacher A. Sequeira), pp. 83–104. Springer Verlag (2010).

[11] T. Bodnár , J. Příhoda . Numerical simulation of turbulent free-surface flow in curved channel. Journal of Flow, Turbulence and Combustion, 76 (4) (2006) 429–442.

[12] T. Bodnár, A. Sequeira Computational and Mathematical Methods in Medicine 2008 83 104

[13] T. Bodnár, A. Sequeira, L. Pirkl. Numerical Simulations of Blood Flow in a Stenosed Vessel under Different Flow Rates using a Generalized Oldroyd - B Model In: Numerical Analysis and Applied Mathematics, Vols 1 and 2. Melville, New York: American Institute of Physics, (2009), vol. 2, pp. 645–648.

[14] T. Bodnár, A. Sequeira, M. Prosi Applied Mathematics and Computation 2011 5055 5067

[15] S.E. Charm, G.S. Kurland Nature 1965 617 618

[16] S. Chien, S. Usami, H.M. Taylor, J.L. Lundberg, M.I. Gregersen Journal of Applied Physiology 1966 81 87

[17] S. Chien, S. Usami, R.J. Dellenback, M.I. Gregersen Science 1967 829 831

[18] S. Chien, S. Usami, R.J. Dellenback, M.I. Gregersen Science 1967 827 829

[19] S. Chien, S. Usami, R. J. Dellenback, M.I. Gregersen American Journal of Physiology 1970 136 142

[20] S. Chien, K.L.P. Sung, R. Skalak, S. Usami, A.L. Tozeren Biophysical Journal 1978 463 487

[21] E.A. Evans, R.M. Hochmuth Biophysical Journal 1976 1 11

[22] Y. Fan, R.I. Tanner, N. Phan-Thien J. Fluid Mech. 2001 327 357

[23] F. Gijsen, F. Van De Vosse, J. Janssen Journal of Biomechanics 1999 601 608

[24] J. Hron, J. Málek, S. Turek Int. J. Numer. Meth. Fluids 2000 863 879

[25] A. Jameson, W.Schmidt, E. Turkel. Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time-stepping scheme. In: AIAA 14th Fluid and Plasma Dynamics Conference, Palo Alto (1981), AIAA paper 81-1259.

[26] A. Leuprecht, K. Perktold Comp. Methods in Biomech. and Biomech. Eng. 2001 149 163

[27] D. Quemada Rheol. Acta 1978 643 653

[28] K.R. Rajagopal, A.R. Srinivasa Journal of Non-Newtonian Fluid Mechanics 2000 207 227

[29] K.R. Rajagopal, A.R. Srinivasa Proc. R. Soc. A 2011 39 58

[30] G.B. Thurston Biophysical Journal 1972 1205 1217

[31] G.B. Thurston Biorheology 1973 375 381

[32] G.B. Thurston Biorheology 1994 179 192

[33] J. Vierendeels, K. Riemslagh, E. Dick J. Comput. Phys. 1999 310 344

Cité par Sources :