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A comparison of non-Newtonian models for lattice Boltzmann blood flow simulations. (English) Zbl 1189.76050
Summary: Three non-Newtonian models for blood are used in a lattice Boltzmann flow solver to simulate non-Newtonian blood flows. Exact analytical solutions for two of these models have been derived and presented for a fully developed 2D channel flow. Original results for the use of the K-L model in addition to the Casson and Carreau-Yasuda models are reported for non-Newtonian flow simulations using a lattice Boltzmann (LB) flow solver. Numerical simulations of non-Newtonian flow in a 2D channel show that these models predict different mass flux and velocity profiles even for the same channel geometry and flow boundary conditions. Which in turn, suggests a more careful model selection for more realistic blood flow simulations. The agreement between predicted velocity profiles and those of exact solutions is excellent, indicating the capability of the LB flow solver for such complex fluid flows.

76A05 Non-Newtonian fluids
76M28 Particle methods and lattice-gas methods
92C35 Physiological flow
Full Text: DOI
[1] Fung, Y.C., Biomechanics, mechanical properties of living tissues, (1993), Springer New York
[2] Luo, X.Y.; Kuang, Z.B., A study on the constitutive equation of blood, Journal of biomechanics, 25, 929, (1992)
[3] Mazumdar, J.N., Biofluid mechanics, (1992), World Scientific Singapore · Zbl 0779.92008
[4] Bird, R.B.; Armstrong, R.C.; Hassager, O., Dynamics of polymer liquids. vol. I. fluid mechanics, (1987), Wiley New York
[5] Chen, S.; Doolen, G.D., Lattice Boltzmann method for fluid flows, Annual review of fluid mechanics, 30, 329, (1998) · Zbl 1398.76180
[6] Succi, S., The lattice Boltzmann method for fluid dynamics and beyond, (2001), Clarendon Press Oxford, UK · Zbl 0990.76001
[7] Wolf-Gladrow, D.A., Lattice-gas cellular automata and lattice Boltzmann models, (2000), Springer New York · Zbl 0999.82054
[8] He, X.; Luo, L.-S., Lattice Boltzmann model for the incompressible navier – stokes equation, Journal of statistical physics, 88, 927, (1997) · Zbl 0939.82042
[9] Sun, C.; Munn, L.L., Particulate nature of blood determines macroscopic rheology: A 2-D lattice Boltzmann analysis, Biophysical journal, 88, 1635, (2005)
[10] Bhatnagar, P.; Gross, E.P.; Krook, M.K., A model for collision processes in gases. I. small amplitude processes in charged and neural one-component systems, Physical review, 94, 3, 511, (1954) · Zbl 0055.23609
[11] Qian, Y.H.; d’humières, D.; Lallemand, P., Lattice BGK models for the navier – stokes equation, Europhysics letters, 17, 479, (1992) · Zbl 1116.76419
[12] Gijsen, F.J.H.; van de Vosse, F.N.; Janssen, J.D., The influence of the non-Newtonian properties of blood on the flow in large arteries: steady flow in carotid bifurcation model, Journal of biomechanics, 32, 601, (1999)
[13] Aharonov, E.; Rothman, D.H., Non-Newtonian flow (through porous-media): A lattice Boltzmann method, Geophysical research letters, 20, 8, 679, (1993)
[14] Gabbanelli, S.; Drazer, G.; Koplik, J., Lattice Boltzmann method for non-Newtonian (power-law) fluids, Physical review E, 72, 4, 046312, (2005)
[15] Kehrwald, D., Lattice Boltzmann simulation of shear thinning fluids, Journal of statistical physics, 121, 223, (2005) · Zbl 1085.82009
[16] Boyd, J.; Buick, J.; Green, S., A second-order accurate lattice Boltzmann non-Newtonian flow model, Journal of physics A, 39, 46, 14241, (2006) · Zbl 1148.82314
[17] Boyd, J.; Buick, J.M.; Green, S., Analysis of the Casson and carreau – yasuda non-Newtonian blood models in steady and oscillatory flows using the lattice Boltzmann method, Physics of fluids, 19, 9, 093103, (2007) · Zbl 1182.76081
[18] Ouared, R.; Chopard, B., Lattice Boltzmann simulation of blood flow: non-Newtonian rheology and clotting processes, Journal of statistical physics, 121, 209, (2005) · Zbl 1108.76089
[19] Boyd, J.; Buick, J.M., Comparison of newtonian and non-Newtonian flows in a two-dimensional carotid artery model using the lattice Boltzmann model, Physics in medicine and biology, 52, 20, 6215, (2007)
[20] J. Bernsdorf, D. Wang, Non-Newtonian blood flow simulation in cerebral aneurysms, Computer & Mathematics with Applications, 2008, in this issue (doi:10.1016/j.camwa.2009.02.019) · Zbl 1189.76801
[21] Malaspinas, O.; Courbebaisse, G.; Deville, M., Simulation of generalized Newtonian fluids with the lattice Boltzmann method, International journal of modern physics C, 18, 12, 1939, (2007) · Zbl 1151.82019
[22] H. Bakhshaei, Lattice Boltzmann simulation of Non-Newtonian fluid flows, M.Sc. Thesis, Dept. of Mech. Eng., Isfahan Univ. of Tech., Isfahan, Iran, 2008
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